- 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

Coherent heat exchange in a prethermalizing open quantum system

Simone Artini1, Mauro Paternostro1,2, and Salvatore Lorenzo1

PDF

Phys. Rev. A 113, 052203 – Published 5 May, 2026

DOI: https://doi.org/10.1103/q5vb-dfgj

Abstract

We investigate a simple model exhibiting a prethermal phase, i.e., a metastable state that emerges before full thermalization, through the framework of quantum stochastic thermodynamics. We explore the effects of quantum coherence in the energy eigenbasis of the initial state of the system on the process of heat exchange with a bath, and their contribution to entropy production as quantified by a heat-exchange fluctuation theorem. Such a relation is derived using the end-point measurement scheme, a protocol that accounts for initial quantum coherence in the statistics of energy exchanges resulting from a nonequilibrium process. We compare these results with those obtained from the widely used two-point measurement scheme, which, by construction, fails to capture such quantum effects.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (29)

  1. G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).
  2. C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78, 2690 (1997).
  3. C. Jarzynski and D. K. Wójcik, Classical and quantum fluctuation theorems for heat exchange, Phys. Rev. Lett. 92, 230602 (2004).
  4. M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009).
  5. S. An, J.-N. Zhang, M. Um, D. Lv, Y. Lu, J. Zhang, Z.-Q. Yin, H. Quan, and K. Kim, Experimental test of the quantum Jarzynski equality with a trapped-ion system, Nat. Phys. 11, 193 (2015).
  6. V. Cimini, S. Gherardini, M. Barbieri, I. Gianani, M. Sbroscia, L. Buffoni, M. Paternostro, and F. Caruso, Experimental characterization of the energetics of quantum logic gates, npj Quantum Inf. 6, 96 (2020).
  7. Z. Zhang, T. Wang, L. Xiang, Z. Jia, P. Duan, W. Cai, Z. Zhan, Z. Zong, J. Wu, L. Sun, et al., Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit, New J. Phys. 20, 085001 (2018).
  8. 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, Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system, Phys. Rev. Lett. 113, 140601 (2014).
  9. M. Lostaglio, A. Belenchia, A. Levy, S. Hernández-Gómez, N. Fabbri, and S. Gherardini, Kirkwood-Dirac quasiprobability approach to quantum fluctuations: Theoretical and experimental perspectives, Quantum 7, 1128 (2023).
  10. M. G. Díaz, G. Guarnieri, and M. Paternostro, Quantum work statistics with initial coherence, Entropy 22, 1223 (2020).
  11. K. Micadei, G. T. Landi, and E. Lutz, Quantum fluctuation theorems beyond two-point measurements, Phys. Rev. Lett. 124, 090602 (2020).
  12. T. Langen, T. Gasenzer, and J. Schmiedmayer, Prethermalization and universal dynamics in near-integrable quantum systems, J. Stat. Mech. (2016) 064009.
  13. B. Bertini, F. H. L. Essler, S. Groha, and N. J. Robinson, Prethermalization and thermalization in models with weak integrability breaking, Phys. Rev. Lett. 115, 180601 (2015).
  14. M. Kollar, F. A. Wolf, and M. Eckstein, Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems, Phys. Rev. B 84, 054304 (2011).
  15. A. Angles-Castillo, M. C. Bañuls, A. Perez, and I. De Vega, Prethermalization of quantum systems interacting with non-equilibrium environments, New J. Phys. 22, 083067 (2020).
  16. M. Marcuzzi, J. Marino, A. Gambassi, and A. Silva, Prethermalization in a nonintegrable quantum spin chain after a quench, Phys. Rev. Lett. 111, 197203 (2013).
  17. M. Marcuzzi, J. Marino, A. Gambassi, and A. Silva, Prethermalization from a low-density Holstein-Primakoff expansion, Phys. Rev. B 94, 214304 (2016).
  18. M. Ueda, Quantum equilibration, thermalization and prethermalization in ultracold atoms, Nat. Rev. Phys. 2, 669 (2020).
  19. S. Saha and R. Bhattacharyya, Prethermalization in an open quantum system coupled to a spatially correlated bosonic bath, J. Stat. Mech. (2024) 023103.
  20. M. Campisi, P. Hänggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
  21. S. Gherardini, A. Belenchia, M. Paternostro, and A. Trombettoni, End-point measurement approach to assess quantum coherence in energy fluctuations, Phys. Rev. A 104, L050203 (2021).
  22. S. Hernández-Gómez, S. Gherardini, A. Belenchia, A. Trombettoni, M. Paternostro, and N. Fabbri, Experimental signature of initial quantum coherence on entropy production, npj Quantum Inf. 9, 86 (2023).
  23. J. Goold and K. Modi, Energetic fluctuations in an open quantum process, AVS Quantum Sci. 3, 045001 (2021).
  24. U. Seifert, Stochastic thermodynamics: Principles and perspectives, Eur. Phys. J. B 64, 423 (2008).
  25. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  26. T. Tomé and M. J. de Oliveira, Entropy production in irreversible systems described by a Fokker-Planck equation, Phys. Rev. E 82, 021120 (2010).
  27. A. Imparato and L. Peliti, The distribution function of entropy flow in stochastic systems, J. Stat. Mech. (2007) L02001.
  28. G. T. Landi and M. Paternostro, Irreversible entropy production: From classical to quantum, Rev. Mod. Phys. 93, 035008 (2021).
  29. S. Artini, M. Paternostro, and S. Lorenzo, Dataset for Coherent heat exchange in a prethermalizing open quantum system [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.19708654.

Outline

Information

Phys. Rev. A 113, 052203– Published 5 May, 2026
  • Received 23 September 2025
  • Accepted 23 April 2026
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