2000 character limit reached
Work Sum Rule for Open Quantum Systems (2402.18855v2)
Published 29 Feb 2024 in quant-ph, cond-mat.mes-hall, and cond-mat.stat-mech
Abstract: A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is nonsingular is based on a partition of Hilbert space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions nontrivially under Hilbert-space partition, and we derive a work sum rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. Our results are illustrated with application to a driven resonant level strongly coupled to a reservoir.
- S. Deffner and S. Campbell, Quantum Thermodynamics, 2053-2571 (Morgan & Claypool Publishers, 2019).
- P. Strasberg, Quantum Stochastic Thermodynamics: Foundations and Selected Applications, Oxford Graduate Texts (Oxford University Press, Oxford, New York, 2022).
- M. Campisi, P. Hänggi, and P. Talkner, Colloquium : Quantum fluctuation relations: Foundations and applications, Reviews of Modern Physics 83, 771 (2011).
- C. Jarzynski, Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale, Annual Review of Condensed Matter Physics 2, 329 (2011).
- A. Shastry, S. Inui, and C. A. Stafford, Scanning tunneling thermometry, Physical Review Applied 13, 024065 (2020).
- J. Liu, K. A. Jung, and D. Segal, Periodically Driven Quantum Thermal Machines from Warming up to Limit Cycle, Physical Review Letters 127, 200602 (2021).
- M. Esposito, M. A. Ochoa, and M. Galperin, Nature of heat in strongly coupled open quantum systems, Physical Review B 92, 235440 (2015).
- P. Haughian, M. Esposito, and T. L. Schmidt, Quantum thermodynamics of the resonant-level model with driven system-bath coupling, Physical Review B 97, 085435 (2018).
- P. Talkner and P. Hänggi, Colloquium : Statistical mechanics and thermodynamics at strong coupling: Quantum and classical, Reviews of Modern Physics 92, 041002 (2020).
- P. Strasberg and A. Winter, First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy, PRX Quantum 2, 030202 (2021).
- N. Bergmann and M. Galperin, A Green’s function perspective on the nonequilibrium thermodynamics of open quantum systems strongly coupled to baths: Nonequilibrium quantum thermodynamics, The European Physical Journal Special Topics 230, 859 (2021).
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2007).
- C. M. Webb and C. A. Stafford, How to Partition a Quantum Observable (2024), arxiv:2402.17908 [quant-ph] .
- C. Jarzynski, Comparison of far-from-equilibrium work relations, Comptes Rendus Physique 8, 495 (2007).
- G. Binnig and H. Rohrer, Scanning tunneling microscopy, Surface Science 126, 236 (1983).
- G. Binnig, C. F. Quate, and Ch. Gerber, Atomic Force Microscope, Physical Review Letters 56, 930 (1986).
- S. Kalinin and A. Gruverman, eds., Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale (Springer, New York, NY, 2007).
- P. Muralt and D. W. Pohl, Scanning tunneling potentiometry, Applied Physics Letters 48, 514 (1986).
- C. C. Williams and H. K. Wickramasinghe, Scanning thermal profiler, Applied Physics Letters 49, 1587 (1986).
- C. A. Stafford, Local temperature of an interacting quantum system far from equilibrium, Physical Review B 93, 245403 (2016).
- A. Shastry and C. A. Stafford, Temperature and voltage measurement in quantum systems far from equilibrium, Physical Review B 94, 155433 (2016).
- S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005).
- M. V. Moskalets, Scattering Matrix Approach to Non-Stationary Quantum Transport (Imperial College Press, 2011).
- C. A. Stafford and A. Shastry, Local entropy of a nonequilibrium fermion system, The Journal of Chemical Physics 146, 092324 (2017).
- A. Shastry, Y. Xu, and C. A. Stafford, The third law of thermodynamics in open quantum systems, The Journal of Chemical Physics 151, 064115 (2019).
- A. Shastry, Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium, Springer Theses (Springer International Publishing, Cham, 2019).
- J. Friedel, Metallic alloys, Il Nuovo Cimento (1955-1965) 7, 287 (1958).
- H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, 2nd ed. (Springer, Berlin ; New York, 2007).
- J. Rammer, Quantum Field Theory of Non-equilibrium States (Cambridge: Cambridge University Press, Cambridge, 2007).
- G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, Cambridge, 2013).
- Ref. [23] uses the convention α→1−α→𝛼1𝛼\alpha\rightarrow 1-\alphaitalic_α → 1 - italic_α.
- The particle number NSsubscript𝑁𝑆N_{S}italic_N start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT that appears in the chemical work term in the First Law [Eq. (42)] is typically independent of α𝛼\alphaitalic_α.
- M. A. Ochoa, A. Bruch, and A. Nitzan, Energy distribution and local fluctuations in strongly coupled open quantum systems: The extended resonant level model, Physical Review B 94, 035420 (2016).
- S. Datta, Chapter 8 - Level broadening, in Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005).
- J. J. Sakurai and J. Napolitano, Modern quantum mechanics; 2nd ed. (Addison-Wesley, San Francisco, CA, 2011) pp. 346–353.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.