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Strong Markov dissipation in driven-dissipative quantum systems (2404.10195v1)

Published 16 Apr 2024 in cond-mat.stat-mech and quant-ph

Abstract: The Lindblad equation, which describes Markovian quantum dynamics under dissipation, is usually derived under the weak system-bath coupling assumption. Strong system-bath coupling often leads to non-Markov evolution. The singular-coupling limit is known as an exception: it yields a Lindblad equation with an arbitrary strength of dissipation. However, the singular-coupling limit requires high-temperature limit of the bath, and hence the system ends up in a trivial infinite-temperature state, which is not desirable in the context of quantum control. In this work, it is shown that we can derive a Markovian Lindblad equation for an arbitrary strength of the system-bath coupling by considering a new scaling limit that is called the singular-driving limit, which combines the singular-coupling limit and fast periodic driving. In contrast to the standard singular-coupling limit, an interplay between dissipation and periodic driving results in a nontrivial steady state.

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References (35)
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Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Oka, T., Kitamura, S.: Floquet engineering of quantum materials. Annu. Rev. Condens. Matter Phys. 10, 387 (2019) https://doi.org/10.1146/annurev-conmatphys-031218-013423 Diehl et al. [2008] Diehl, S., Micheli, A., Kantian, A., Kraus, B., Büchler, H.P., Zoller, P.: Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008) https://doi.org/10.1038/nphys1073 Verstraete et al. [2009] Verstraete, F., Wolf, M.M., Ignacio Cirac, J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009) https://doi.org/10.1038/nphys1342 Breuer and Petruccione [2002] Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Diehl, S., Micheli, A., Kantian, A., Kraus, B., Büchler, H.P., Zoller, P.: Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008) https://doi.org/10.1038/nphys1073 Verstraete et al. [2009] Verstraete, F., Wolf, M.M., Ignacio Cirac, J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009) https://doi.org/10.1038/nphys1342 Breuer and Petruccione [2002] Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Verstraete, F., Wolf, M.M., Ignacio Cirac, J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009) https://doi.org/10.1038/nphys1342 Breuer and Petruccione [2002] Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. 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[2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Diehl, S., Micheli, A., Kantian, A., Kraus, B., Büchler, H.P., Zoller, P.: Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008) https://doi.org/10.1038/nphys1073 Verstraete et al. [2009] Verstraete, F., Wolf, M.M., Ignacio Cirac, J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009) https://doi.org/10.1038/nphys1342 Breuer and Petruccione [2002] Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Verstraete, F., Wolf, M.M., Ignacio Cirac, J.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009) https://doi.org/10.1038/nphys1342 Breuer and Petruccione [2002] Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. 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Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. 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Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. 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B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. 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[2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, New York (2002) Gorini et al. [1976] Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976) https://doi.org/10.1063/1.522979 Lindblad [1976] Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976) https://doi.org/10.1007/BF01608499 De Vega and Alonso [2017] De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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[2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 De Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017) https://doi.org/10.1103/RevModPhys.89.015001 Wichterich et al. [2007] Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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[2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. 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Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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[2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Wichterich, H., Henrich, M.J., Breuer, H.P., Gemmer, J., Michel, M.: Modeling heat transport through completely positive maps. Phys. Rev. E 76, 031115 (2007) https://doi.org/10.1103/PhysRevE.76.031115 Schaller and Brandes [2008] Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Schaller, G., Brandes, T.: Preservation of positivity by dynamical coarse graining. Phys. Rev. A 78, 022106 (2008) https://doi.org/10.1103/PhysRevA.78.022106 Benatti et al. [2010] Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. 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[2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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[2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. 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Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. 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Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Benatti, F., Floreanini, R., Marzolino, U.: Entangling two unequal atoms through a common bath. Phys. Rev. A 81, 012105 (2010) https://doi.org/10.1103/PhysRevA.81.012105 Kiršanskas et al. [2018] Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. 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A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kiršanskas, G., Franckié, M., Wacker, A.: Phenomenological position and energy resolving Lindblad approach to quantum kinetics. Phys. Rev. B 97, 035432 (2018) https://doi.org/10.1103/PhysRevB.97.035432 Nathan and Rudner [2020] Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Nathan, F., Rudner, M.S.: Universal Lindblad equation for open quantum systems. Phys. Rev. B 102, 115109 (2020) https://doi.org/10.1103/PhysRevB.102.115109 Becker et al. [2021] Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. 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[2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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[2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Becker, T., Wu, L.N., Eckardt, A.: Lindbladian approximation beyond ultraweak coupling. Phys. Rev. E 104, 014110 (2021) https://doi.org/10.1103/PhysRevE.104.014110 Mori [2023] Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. 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Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
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E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. 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Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  15. Mori, T.: Floquet States in Open Quantum Systems. Annu. Rev. Condens. Matter Phys. 14, 35 (2023) https://doi.org/10.1146/annurev-conmatphys-040721-015537 Mori et al. [2016] Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  16. Mori, T., Kuwahara, T., Saito, K.: Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. Phys. Rev. Lett. 116, 120401 (2016) https://doi.org/10.1103/PhysRevLett.116.120401 Kuwahara et al. [2016] Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  17. Kuwahara, T., Mori, T., Saito, K.: Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems. Ann. Phys. (N. Y). 367, 96 (2016) https://doi.org/10.1016/j.aop.2016.01.012 Abanin et al. [2017a] Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Abanin, D.A., De Roeck, W., Ho, W.W., Huveneers, F.: Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems. Phys. Rev. B 95, 014112 (2017) https://doi.org/10.1103/PhysRevB.95.014112 Abanin et al. [2017b] Abanin, D., De Roeck, W., Ho, W.W., Huveneers, F.: A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809 (2017) https://doi.org/10.1007/s00220-017-2930-x D’Alessio et al. [2016] D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. 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[2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 D’Alessio, L., Kafri, Y., Polkovnikov, A., Rigol, M.: From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239 (2016) https://doi.org/10.1080/00018732.2016.1198134 Mori et al. [2018] Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. 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[2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
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Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Ikeda, T.N., Kaminishi, E., Ueda, M.: Thermalization and prethermalization in isolated quantum systems: A theoretical overview. J. Phys. B At. Mol. Opt. Phys. 51, 112001 (2018) https://doi.org/10.1088/1361-6455/aabcdf Shirai and Mori [2020] Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. 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Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T.: Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys. Rev. E 101, 042116 (2020) https://doi.org/10.1103/physreve.101.042116 Breuer et al. [2000] Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Breuer, H.P., Huber, W., Petruccione, F.: Quasistationary distributions of dissipative nonlinear quantum oscillators in strong periodic driving fields. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 61, 4883 (2000) https://doi.org/10.1103/PhysRevE.61.4883 Kohn [2001] Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kohn, W.: Periodic thermodynamics. J. Stat. Phys. 103, 417 (2001) https://doi.org/10.1023/A:1010327828445 Shirai et al. [2015] Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Mori, T., Miyashita, S.: Condition for emergence of the Floquet-Gibbs state in periodically driven open systems. Phys. Rev. E 91, 030101 (2015) https://doi.org/10.1103/PhysRevE.91.030101 Shirai et al. [2016] Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. 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[2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. 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[2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. 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X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. 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  26. Shirai, T., Thingna, J., Mori, T., Denisov, S., Hänggi, P., Miyashita, S.: Effective Floquet-Gibbs states for dissipative quantum systems. New J. Phys. 18, 1–13 (2016) https://doi.org/10.1088/1367-2630/18/5/053008 Palmer [1977] Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. 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Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Palmer, P.F.: The singular coupling and weak coupling limits. J. Math. Phys. 18(3), 527–529 (1977) https://doi.org/10.1063/1.523296 Hepp and Lieb [1973] Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. Acta 46, 573 (1973) https://doi.org/10.5169/seals-114496 Kraus et al. [2008] Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Hepp, K., Lieb, E.H.: Phase transitions in reservoir-driven open systems with applications to lasers and superconductors. Helv. Phys. 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Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kraus, B., Büchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008) https://doi.org/10.1103/PhysRevA.78.042307 Seifert [2016] Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Seifert, U.: First and Second Law of Thermodynamics at Strong Coupling. Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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Phys. Rev. Lett. 116, 020601 (2016) https://doi.org/10.1103/PhysRevLett.116.020601 Jarzynski [2017] Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. 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Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
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Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
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  31. Jarzynski, C.: Stochastic and macroscopic thermodynamics of strongly coupled systems. Phys. Rev. X 7, 011008 (2017) https://doi.org/10.1103/PhysRevX.7.011008 Kirkwood [1935] Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  32. Kirkwood, J.G.: Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 3, 300 (1935) https://doi.org/10.1063/1.1749657 Jarzynski [2004] Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  33. Jarzynski, C.: Nonequilibrium work theorem for a system strongly coupled to a thermal environment. J. Stat. Mech. Theory Exp. 2004, 09005 (2004) https://doi.org/10.1088/1742-5468/2004/09/P09005 Mori and Miyashita [2008] Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  34. Mori, T., Miyashita, S.: Dynamics of the density matrix in contact with a thermal bath and the quantum master equation. J. Phys. Soc. Japan 77, 124005 (2008) https://doi.org/10.1143/JPSJ.77.124005 Cresser and Anders [2021] Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601 Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601
  35. Cresser, J.D., Anders, J.: Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State. Phys. Rev. Lett. 127, 250601 (2021) https://doi.org/10.1103/PhysRevLett.127.250601

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