Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir (2307.06679v3)

Published 13 Jul 2023 in cond-mat.stat-mech and quant-ph

Abstract: In nano-scale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work and entropy production in such systems is however missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctuating temperature of the reservoir. Based on a fluctuation theorem, we identify the appropriate entropy production that results in a thermodynamically consistent statistical description. We illustrate our results by analyzing the work production for a finite-size reservoir Szilard engine.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (41)
  1. R. J. Harris and G. M. Schütz, Fluctuation theorems for stochastic dynamics, J. Stat. Mech: Theory Exp. 2007, P07020 (2007).
  2. C. Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Annu. Rev. Condens. Matter Phys. 2, 329 (2011).
  3. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  4. G. N. Bochkov and Y. E. Kuzovlev, Fluctuation-dissipation relations. achievements and misunderstandings, Phys. Usp. 56, 590 (2013).
  5. C. van den Broeck and M. Esposito, Ensemble and trajectory thermodynamics: A brief introduction, Phys. A: Stat. Mech. 418, 6 (2015).
  6. M. M. Mansour and F. Baras, Fluctuation theorem: A critical review, Chaos 27, 104609 (2017).
  7. U. Seifert, From stochastic thermodynamics to thermodynamic inference, Annu. Rev. Condens. Matter Phys. 10, 171 (2019).
  8. U. Seifert, Entropy production along a stochastic trajectory and an integral fluctuation theorem, Phys. Rev. Lett. 95, 040602 (2005).
  9. G. N. Bochkov and Y. E. Kuzovlev, Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. generalized fluctuation-dissipation theorem, Physica A 106, 443 (1981a).
  10. G. N. Bochkov and Y. E. Kuzovlev, Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. kinetic potential and variational principles for nonlinear irreversible processes, Physica A 106, 480 (1981b).
  11. G. E. Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys. 90, 1481 (1998).
  12. G. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).
  13. G. E. Crooks, Path-ensemble averages in systems driven far from equilibrium, Phys. Rev. E 61, 2361 (2000).
  14. C. Jarzynski, Hamiltonian derivation of a detailed fluctuation theorem, J. Stat. Phys. 98, 77 (2000).
  15. U. Seifert, Fluctuation theorem for birth–death or chemical master equations with time-dependent rates, J. Phys. A: Math. Gen. 37, L517 (2004).
  16. C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78, 2690 (1997a).
  17. C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys. Rev. E 56, 5018 (1997b).
  18. A. E. Rastegin, Non-equilibrium equalities with unital quantum channels, J. Stat. Mech. 2013, P06016 (2013).
  19. G. Hummer and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl. Acad. Sci. USA 98, 3658 (2001).
  20. G. Hummer and A. Szabo, Free energy profiles from single-molecule pulling experiments, Proc. Natl. Acad. Sci. USA 107, 21441 (2010).
  21. Y. Watanabe, R. B. Capaz, and R. A. Simao, Surface characterization using friction force microscopy and the Jarzynski equality, Appl. Surf. Sci. 607, 155070 (2023).
  22. J. P. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021).
  23. G. Schaller, C. Nietner, and T. Brandes, Relaxation dynamics of meso-reservoirs, New J. Phys. 16, 125011 (2014).
  24. C. Grenier, C. Kollath, and A. Georges, Thermoelectric transport and peltier cooling of cold atomic gases, C. R. Phys. 17, 1161 (2016).
  25. Y.-H. Ma, Optimizing thermodynamic cycles with two finite-sized reservoirs, Entropy 22, 1002 (2020).
  26. H. Yuan, Y.-H. Ma, and C. P. Sun, Optimizing thermodynamic cycles with two finite-sized reservoirs, Phys. Rev. E 105, L022101 (2022).
  27. A. Riera-Campeny, A. Sanpera, and P. Strasberg, Quantum systems correlated with a finite bath: Nonequilibrium dynamics and thermodynamics, PRX Quantum 2, 010340 (2021).
  28. 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).
  29. P. Strasberg, M. G. Díaz, and A. Riera-Campeny, Clausius inequality for finite baths reveals universal efficiency improvements, Phys. Rev. E 104, L022103 (2021).
  30. C. Elouard and C. Lombard Latune, Extending the laws of thermodynamics for arbitrary autonomous quantum systems, PRX Quantum 4, 020309 (2023).
  31. T. L. van den Berg, F. Brange, and P. Samuelsson, Energy and temperature fluctuations in the single electron box, New J. Phys. 17, 075012 (2015).
  32. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
  33. R. Clausius, Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie, Ann. Phys. 201, 353 (1865).
  34. M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010).
  35. D. Reeb and M. M. Wolf, An improved Landauer principle with finite-size corrections, New J. Phys. 16, 103011 (2014).
  36. G. Manzano, Squeezed thermal reservoir as a generalized equilibrium reservoir, Phys. Rev. E 98, 042123 (2018).
  37. M. Esposito and P. Gaspard, Quantum master equation for a system influencing its environment, Phys. Rev. E 68, 066112 (2003).
  38. H.-P. Breuer, J. Gemmer, and M. Michel, Non-Markovian quantum dynamics: Correlated projection superoperators and hilbert space averaging, Phys. Rev. E 73, 016139 (2006).
  39. M. Esposito and P. Gaspard, Quantum master equation for the microcanonical ensemble, Phys. Rev. E 76, 041134 (2007).
  40. H.-P. Breuer, Non-Markovian generalization of the lindblad theory of open quantum systems, Phys. Rev. A 75, 022103 (2007).
  41. A. Riera-Campeny, A. Sanpera, and P. Strasberg, Open quantum systems coupled to finite baths: A hierarchy of master equations, Phys. Rev. E 105, 054119 (2022).
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets