- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems

Irene Ada Picatoste1, Alessandra Colla2,3, and Heinz-Peter Breuer1,4

PDF

Phys. Rev. A 112, 022210 – Published 12 August, 2025

DOI: https://doi.org/10.1103/kbsf-x4bz

Abstract

We study the nonequilibrium thermodynamics of pure decoherence processes in open quantum systems coupled to a thermal reservoir. We review various definitions of central quantities, such as internal energy, work, heat, and entropy production, developed within local and global approaches to quantum thermodynamics. Within local approaches, thermodynamic quantities only refer to the open system's degrees of freedom, while in the global approaches, certain quantities are defined by referring explicitly to the reservoir degrees of freedom. Employing a microscopic, analytically solvable model, we perform a comparison of these two perspectives, revealing substantial differences in the thermodynamic quantities and in the formulations of the first and second laws. The main reason for these discrepancies is the fact that the global approaches involve the system-reservoir interaction which exchanges a large amount of energy with the environment, while the average open system energy is constant in time because the dynamics represents pure decoherence and does not affect the open system populations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. J. Gemmer, M. Michel, and G. Mahler, Quantum Thermodynamics (Springer, Berlin, 2004).
  2. F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime (Springer, Cham, Switzerland, 2018).
  3. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
  4. M. Esposito, K. Lindenberg, and C. V. den Broeck, New J. Phys. 12, 013013 (2010).
  5. A. Colla, Dynamically emergent quantum thermodynamics of open systems, Ph.D. thesis, Freiburg, 2024, https://freidok.uni-freiburg.de/data/263695.
  6. P. Strasberg, M. G. Díaz, and A. Riera-Campeny, Phys. Rev. E 104, L022103 (2021).
  7. S. Deffner and E. Lutz, Phys. Rev. Lett. 105, 170402 (2010).
  8. F. Nicacio and R. N. P. Maia, Phys. Rev. A 108, 022209 (2023).
  9. G. T. Landi and M. Paternostro, Rev. Mod. Phys. 93, 035008 (2021).
  10. A. Rivas, Phys. Rev. Lett. 124, 160601 (2020).
  11. C. Elouard and C. Lombard Latune, PRX Quantum 4, 020309 (2023).
  12. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics, Vol. 286 (Springer, Berlin, 1987).
  13. A. Colla and H.-P. Breuer, Phys. Rev. A 105, 052216 (2022).
  14. H. Spohn, J. Math. Phys. 19, 1227 (1978) .
  15. M. Popovic, M. T. Mitchison, and J. Goold, Proc. R. Soc. A 479, 20230040 (2023).
  16. S. Marcantoni, J. Phys.: Conf. Ser. 841, 012019 (2017).
  17. A. Colla, N. Neubrand, and H.-P. Breuer, New J. Phys. 24, 123005 (2022).
  18. B. Vacchini and G. Amato, Sci. Rep. 6, 37328 (2016).
  19. S. Alipour, A. T. Rezakhani, A. P. Babu, K. Mølmer, M. Möttönen, and T. Ala-Nissila, Phys. Rev. X 10, 041024 (2020).
  20. F. Shibata, Y. Takahashi, and N. Hashitsume, J. Stat. Phys. 17, 171 (1977).
  21. S. Chaturvedi and F. Shibata, Z. Phys. B 35, 297 (1979).
  22. M. J. W. Hall, J. D. Cresser, L. Li, and E. Andersson, Phys. Rev. A 89, 042120 (2014).
  23. H.-P. Breuer, B. Kappler, and F. Petruccione, Phys. Rev. A 59, 1633 (1999).
  24. H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Rev. Mod. Phys. 88, 021002 (2016).
  25. P. Strasberg and M. Esposito, Phys. Rev. E 99, 012120 (2019).
  26. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Springer, Basel, Switzerland, 1992).
  27. P. Hayden and J. Sorce, J. Phys. A: Math. Theor. 55, 225302 (2022).
  28. A. Colla, H.-P. Breuer, and G. Gasbarri, arXiv:2506.04097.
  29. R. Alicki, J. Phys. A: Math. Gen. 12, L103 (1979).
  30. A. Colla, F. Hasse, D. Palani, T. Schaetz, H.-P. Breuer, and U. Warring, Nat. Commun. 16, 2502 (2025).
  31. E. Davies, Commun. Marh. Phys. 39, 91 (1974).
  32. A. Colla and H.-P. Breuer, Quantum Sci. Technol. 10, 015047 (2025).
  33. D. Chruściński, Phys. Rep. 992, 1 (2022).
  34. V. G. Morozov and G. Röpke, Condens. Matter Phys. 15, 43004 (2012).
  35. H. Spohn and J. L. Lebowitz, Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs, in Advances in Chemical Physics (Wiley, New York, 1978), pp. 109–142.
  36. A. Serafini, Quantum Continuous Variables: A Primer of Theoretical Methods (Taylor & Francis, Andover, UK, 2017).
  37. I. A. Picatoste, A. Colla, and H.-P. Breuer, Phys. Rev. Res. 6, 013258 (2024).
  38. M. Ban, S. Kitajima, and F. Shibata, Phys. Lett. A 374, 2324 (2010).
  39. R. Doll, D. Zueco, M. Wubs, S. Kohler, and P. Hänggi, Chem. Phys. 347, 243 (2008).
  40. S. Wißmann, Non-Markovian quantum probes for complex systems, Ph.D. thesis, Freiburg, 2016, https://freidok.uni-freiburg.de/data/11335.

Outline

Information

Phys. Rev. A 112, 022210– Published 12 August, 2025
  • Received 12 June 2025
  • Accepted 23 July 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation