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Quantum stochastic thermodynamics in the mesoscopic-leads formulation

Laetitia P. Bettmann1,*, Michael J. Kewming1,†, Gabriel T. Landi2,‡, John Goold1,3,§, and Mark T. Mitchison1,3,4,∥

  • 1School of Physics, Trinity College Dublin, College Green, Dublin 2, D02K8N4, Ireland
  • 2Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
  • 3Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2, D02YN67, Ireland
  • 4Department of Physics, King's College London, Strand, London, WC2R 2LS, United Kingdom

  • *Contact author: bettmanl@tcd.ie
  • †Contact author: kewmingm@tcd.ie
  • ‡Contact author: glandi@ur.rochester.edu
  • §Contact author: gooldj@tcd.ie
  • ∥Contact author: mark.mitchison@tcd.ie
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Phys. Rev. E 112, 014105 – Published 7 July, 2025

DOI: https://doi.org/10.1103/3msj-9qgb

Abstract

We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.

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References (105)

  1. U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).
  2. S. Ciliberto, Phys. Rev. X 7, 021051 (2017).
  3. U. Seifert, Phys. A: Stat. Mech. Appl. 504, 176 (2018).
  4. U. Seifert, Phys. Rev. Lett. 95, 040602 (2005).
  5. J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95, 333 (1999).
  6. C. Jarzynski, Annu. Rev. Condens. Matter Phys. 2, 329 (2011).
  7. J. M. Horowitz, Phys. Rev. E 85, 031110 (2012).
  8. F. W. J. Hekking and J. P. Pekola, Phys. Rev. Lett. 111, 093602 (2013).
  9. G. Manzano and R. Zambrini, AVS Quantum Sci. 4, 025302 (2022).
  10. G. Manzano, R. Fazio, and E. Roldàn, Phys. Rev. Lett. 122, 220602 (2019).
  11. J. Goold, M. Huber, A. Riera, L. d. Rio, and P. Skrzypczyk, J. Phys. A: Math. Theor. 49, 143001 (2016).
  12. K. Sekimoto, Stochastic Energetics, Lecture Notes in Physics, Vol. 799 (Springer, Berlin, Germany, 2010).
  13. M. Esposito, U. Harbola, and S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009).
  14. M. Campisi, P. Hänggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011).
  15. S. Deffner and E. Lutz, Phys. Rev. Lett. 107, 140404 (2011).
  16. Y. Morikuni and H. Tasaki, J. Stat. Phys. 143, 1 (2011).
  17. K. Funo, Y. Murashita, and M. Ueda, New J. Phys. 17, 075005 (2015).
  18. G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Phys. Rev. X 8, 031037 (2018).
  19. A. Bartolotta and S. Deffner, Phys. Rev. X 8, 011033 (2018).
  20. T. B. Batalhão, A. M. Souza, L. Mazzola, R. Auccaise, R. S. Sarthour, I. S. Oliveira, J. Goold, G. De Chiara, M. Paternostro, and R. M. Serra, Phys. Rev. Lett. 113, 140601 (2014).
  21. S. An, J.-N. Zhang, M. Um, D. Lv, Y. Lu, J. Zhang, Z.-Q. Yin, H. T. Quan, and K. Kim, Nat. Phys. 11, 193 (2015).
  22. P. Talkner and P. Hänggi, Rev. Mod. Phys. 92, 041002 (2020).
  23. Y. M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000).
  24. B. K. Agarwalla, B. Li, and J.-S. Wang, Phys. Rev. E 85, 051142 (2012).
  25. M. Esposito, M. A. Ochoa, and M. Galperin, Phys. Rev. B 91, 115417 (2015).
  26. M. Moskalets and M. Büttiker, Phys. Rev. B 70, 245305 (2004).
  27. M. Moskalets, Phys. Rev. Lett. 112, 206801 (2014).
  28. E. Potanina, C. Flindt, M. Moskalets, and K. Brandner, Phys. Rev. X 11, 021013 (2021).
  29. E. Aurell, Phys. Rev. E 97, 062117 (2018).
  30. K. Funo and H. T. Quan, Phys. Rev. E 98, 012113 (2018).
  31. K. Funo and H. T. Quan, Phys. Rev. Lett. 121, 040602 (2018).
  32. M. Kilgour, B. K. Agarwalla, and D. Segal, J. Chem. Phys. 150, 084111 (2019).
  33. M. Popovic, M. T. Mitchison, A. Strathearn, B. W. Lovett, J. Goold, and P. R. Eastham, PRX Quantum 2, 020338 (2021).
  34. G. E. Fux, D. Kilda, B. W. Lovett, and J. Keeling, Phys. Rev. Res. 5, 033078 (2023).
  35. M. P. Woods, R. Groux, A. W. Chin, S. F. Huelga, and M. B. Plenio, J. Math. Phys. 55, 032101 (2014).
  36. J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014).
  37. P. Strasberg, G. Schaller, N. Lambert, and T. Brandes, New J. Phys. 18, 073007 (2016).
  38. D. Newman, F. Mintert, and A. Nazir, Phys. Rev. E 95, 032139 (2017).
  39. N. Anto-Sztrikacs and D. Segal, New J. Phys. 23, 063036 (2021).
  40. O. Diba, H. J. D. Miller, J. Iles-Smith, and A. Nazir, Phys. Rev. Lett. 132, 190401 (2024).
  41. J. E. Subotnik, T. Hansen, M. A. Ratner, and A. Nitzan, J. Chem. Phys. 130, 144105 (2009).
  42. A. M. Lacerda, M. J. Kewming, M. Brenes, C. Jackson, S. R. Clark, M. T. Mitchison, and J. Goold, Phys. Rev. E 110, 014125 (2024).
  43. A. M. Lacerda, A. Purkayastha, M. Kewming, G. T. Landi, and J. Goold, Phys. Rev. B 107, 195117 (2023).
  44. D. Gruss, K. A. Velizhanin, and M. Zwolak, Sci. Rep. 6, 24514 (2016).
  45. P. H. Guimarães, G. T. Landi, and M. J. de Oliveira, Phys. Rev. E 94, 032139 (2016).
  46. J. E. Elenewski, D. Gruss, and M. Zwolak, J. Chem. Phys. 147, 151101 (2017).
  47. R. Uzdin, S. Gasparinetti, R. Ozeri, and R. Kosloff, New J. Phys. 20, 063030 (2018).
  48. I. Reichental, A. Klempner, Y. Kafri, and D. Podolsky, Phys. Rev. B 97, 134301 (2018).
  49. F. Chen, E. Arrigoni, and M. Galperin, New J. Phys. 21, 123035 (2019).
  50. M. Brenes, J. J. Mendoza-Arenas, A. Purkayastha, M. T. Mitchison, S. R. Clark, and J. Goold, Phys. Rev. X 10, 031040 (2020).
  51. A. A. Dzhioev and D. S. Kosov, J. Chem. Phys. 134, 044121 (2011).
  52. S. Ajisaka, F. Barra, C. Mejía-Monasterio, and T. Prosen, Phys. Rev. B 86, 125111 (2012).
  53. S. Ajisaka and F. Barra, Phys. Rev. B 87, 195114 (2013).
  54. T. Zelovich, L. Kronik, and O. Hod, J. Chem. Theory Comput. 10, 2927 (2014).
  55. L. Chen, T. Hansen, and I. Franco, J. Phys. Chem. C 118, 20009 (2014).
  56. A. Oz, O. Hod, and A. Nitzan, J. Chem. Theory Comput. 16, 1232 (2020).
  57. F. Schwarz, M. Goldstein, A. Dorda, E. Arrigoni, A. Weichselbaum, and J. von Delft, Phys. Rev. B 94, 155142 (2016).
  58. F. Schwarz, I. Weymann, J. von Delft, and A. Weichselbaum, Phys. Rev. Lett. 121, 137702 (2018).
  59. M. Lotem, A. Weichselbaum, J. von Delft, and M. Goldstein, Phys. Rev. Res. 2, 043052 (2020).
  60. J. E. Elenewski, G. Wójtowicz, M. M. Rams, and M. Zwolak, J. Chem. Phys. 155, 124117 (2021).
  61. G. Wójtowicz, J. E. Elenewski, M. M. Rams, and M. Zwolak, Phys. Rev. B 104, 165131 (2021).
  62. A. Imamoglu, Phys. Rev. A 50, 3650 (1994).
  63. B. M. Garraway, Phys. Rev. A 55, 4636 (1997).
  64. B. M. Garraway, Phys. Rev. A 55, 2290 (1997).
  65. D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 120, 030402 (2018).
  66. N. Lambert, S. Ahmed, M. Cirio, and F. Nori, Nat. Commun. 10, 3721 (2019).
  67. F. Mascherpa, A. Smirne, A. D. Somoza, P. Fernández-Acebal, S. Donadi, D. Tamascelli, S. F. Huelga, and M. B. Plenio, Phys. Rev. A 101, 052108 (2020).
  68. M. Brenes, G. Guarnieri, A. Purkayastha, J. Eisert, D. Segal, and G. Landi, Phys. Rev. B 108, L081119 (2023).
  69. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
  70. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
  71. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, UK, 2009).
  72. G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, PRX Quantum 5, 020201 (2024).
  73. H. J. D. Miller, G. Guarnieri, M. T. Mitchison, and J. Goold, Phys. Rev. Lett. 125, 160602 (2020).
  74. T. Van Vu and K. Saito, Phys. Rev. Lett. 128, 010602 (2022).
  75. A. Rolandi and M. Perarnau-Llobet, Quantum 7, 1161 (2023).
  76. D. Gruss, A. Smolyanitsky, and M. Zwolak, J. Chem. Phys. 147, 141102 (2017).
  77. G. Wójtowicz, J. E. Elenewski, M. M. Rams, and M. Zwolak, Phys. Rev. A 101, 050301(R) (2020).
  78. A. M. Lyapunov and J. A. Walker, J. Appl. Mech. 61, 226 (1994).
  79. M. Coppola, D. Karevski, and G. T. Landi, Phys. Rev. B 110, 094315 (2024).
  80. S. Bravyi, Quantum Inf. Comput. 5, 216 (2005).
  81. G. C. Wick, Phys. Rev. 80, 268 (1950).
  82. G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Phys. Rev. E 92, 032129 (2015).
  83. A. Levy and R. Kosloff, Europhys. Lett. 107, 20004 (2014).
  84. C. Elouard, D. A. Herrera-Martí, M. Clusel, and A. Auffèves, npj Quantum Inf. 3, 9 (2017).
  85. G. D. Chiara, G. Landi, A. Hewgill, B. Reid, A. Ferraro, A. J. Roncaglia, and M. Antezza, New J. Phys. 20, 113024 (2018).
  86. D. J. Evans and D. J. Searles, Adv. Phys. 51, 1529 (2002).
  87. M. Campisi, J. Phys. A: Math. Theor. 47, 245001 (2014).
  88. G. E. Crooks, Phys. Rev. E 60, 2721 (1999).
  89. M. Ferri-Cortés, J. A. Almanza-Marrero, R. López, R. Zambrini, and G. Manzano, Phys. Rev. Res. 7, 013077 (2025).
  90. D. A. Abanin and L. S. Levitov, Phys. Rev. Lett. 94, 186803 (2005).
  91. I. Klich, arXiv:cond-mat/0209642.
  92. M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104, 090601 (2010).
  93. Y.-Z. Zhen, D. Egloff, K. Modi, and O. Dahlsten, Phys. Rev. Lett. 127, 190602 (2021).
  94. S. Dago and L. Bellon, Phys. Rev. Lett. 128, 070604 (2022).
  95. L. Banchi, P. Giorda, and P. Zanardi, Phys. Rev. E 89, 022102 (2014).
  96. H. J. Carmichael and D. F. Walls, J. Phys. A 6, 1552 (1973).
  97. H. Wichterich, M. J. Henrich, H.-P. Breuer, J. Gemmer, and M. Michel, Phys. Rev. E 76, 031115 (2007).
  98. A. Rivas, A. D. K. Plato, S. F. Huelga, and M. B. Plenio, New J. Phys. 12, 113032 (2010).
  99. F. Barra, Sci. Rep. 5, 14873 (2015).
  100. A. S. Trushechkin and I. V. Volovich, Europhys. Lett. 113, 30005 (2016).
  101. J. O. González, L. A. Correa, G. Nocerino, J. P. Palao, D. Alonso, and G. Adesso, Open Syst. Inf. Dynam. 24, 1740010 (2017).
  102. P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, New J. Phys. 19, 123037 (2017).
  103. M. T. Naseem, A. Xuereb, and Ö. E. Müstecaplioğlu, Phys. Rev. A 98, 052123 (2018).
  104. M. T. Mitchison and M. B. Plenio, New J. Phys. 20, 033005 (2018).
  105. D. Tupkary, A. Dhar, M. Kulkarni, and A. Purkayastha, Phys. Rev. A 105, 032208 (2022).

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Phys. Rev. E 112, 014105– Published 7 July, 2025
  • Received 6 March 2025
  • Accepted 5 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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