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Impact of information on quantum heat engines

Lindsay Bassman Oftelie and Michele Campisi

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Phys. Rev. A 113, 052453 – Published 26 May, 2026

DOI: https://doi.org/10.1103/t1wl-p415

Abstract

The emerging field of quantum thermodynamics is beginning to reveal the intriguing role that information can play in quantum thermal engines. Information enters as a resource when considering feedback-controlled thermal machines. While both a general theory of quantum feedback control as well as specific examples of quantum feedback-controlled engines have been presented, still lacking is a general framework for such machines. Here, we present a framework for a generic, two-stroke quantum heat engine interacting with N thermal baths and Maxwell's demon. The demon performs projective measurements on the engine working substance, the outcome of which is recorded in a classical memory, embedded in its own thermal bath. To perform feedback control, the demon enacts unitary operations on the working substance, conditioned on the recorded outcome. By accounting for the thermodynamic cost of measurement, and hence considering the machine-memory compound as a hybrid (quantum-classical) standard thermal machine interacting with N+1 thermal baths, our framework puts the working substance and memory on equal footing, thereby enabling a comprehensible resolution to Maxwell's paradox and elucidating the intricate manner in which information impacts the performance of quantum engines. We illustrate the application of our framework with a two-qubit engine. A remarkable observation is that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.

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References (59)

  1. in Quantum Thermodynamics, edited by J. Gemmer, M. Michel, and G. Mahler, Lecture Notes in Physics Vol. 784 (Springer-Verlag, Berlin, 2009).
  2. F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics Vol. 195 (Springer, New York, 2018).
  3. S. Deffner and S. Campbell, Quantum Thermodynamics: An Introduction to the Thermodynamics of Quantum Information (Morgan and Claypool, San Rafael, California, USA, 2019).
  4. P. Strasberg, Quantum Stochastic Thermodynamics Foundations and Selected Applications, Oxford Graduate Texts (Oxford University, New York, 2022).
  5. S. Campbell, I. D'Amico, M. A. Ciampini, J. Anders, N. Ares, S. Artini, A. Auffeves, L. B. Oftelie, L. Bettman, M. V. Bonança, T. Busch, M. Campisi, M. F. Cavalcante, L. A. Correa, E. Cuestas, C. B. Dag, D. Salambô, S. Deffner, A. del Campo, A. Deutschmann-Olek, et al., Roadmap on quantum thermodynamics, Quantum Sci. Technol. 11, 012501 (2025).
  6. H.-T. Quan, Y.-X. Liu, C.-P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E 76, 031105 (2007).
  7. T. Denzler and E. Lutz, Efficiency fluctuations of a quantum heat engine, Phys. Rev. Res. 2, 032062(R) (2020).
  8. A. Solfanelli, G. Giachetti, M. Campisi, S. Ruffo, and N. Defenu, Quantum heat engine with long-range advantages, New J. Phys. 25, 033030 (2023).
  9. A. Levy and R. Kosloff, Quantum absorption refrigerator, Phys. Rev. Lett. 108, 070604 (2012).
  10. N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, and P. Skrzypczyk, Entanglement enhances cooling in microscopic quantum refrigerators, Phys. Rev. E 89, 032115 (2014).
  11. R. Kosloff and A. Levy, Quantum heat engines and refrigerators: Continuous devices, Annu. Rev. Phys. Chem. 65, 365 (2014).
  12. M. Campisi, J. Pekola, and R. Fazio, Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments, New J. Phys. 17, 035012 (2015).
  13. H. Tajima and K. Funo, Superconducting-like heat current: Effective cancellation of current-dissipation trade-off by quantum coherence, Phys. Rev. Lett. 127, 190604 (2021).
  14. S. Kamimura, H. Hakoshima, Y. Matsuzaki, K. Yoshida, and Y. Tokura, Quantum-enhanced heat engine based on superabsorption, Phys. Rev. Lett. 128, 180602 (2022).
  15. L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Phys. Rep. 1087, 1 (2024).
  16. J. J. Park, K.-H. Kim, T. Sagawa, and S. W. Kim, Heat engine driven by purely quantum information, Phys. Rev. Lett. 111, 230402 (2013).
  17. K. Brandner, M. Bauer, M. T. Schmid, and U. Seifert, Coherence-enhanced efficiency of feedback-driven quantum engines, New J. Phys. 17, 065006 (2015).
  18. C. Elouard and A. N. Jordan, Efficient quantum measurement engines, Phys. Rev. Lett. 120, 260601 (2018).
  19. J. C. Maxwell, Theory of Heat (Appleton, London, 1871).
  20. L. Szilard, Über die entropieverminderung in einem thermodynamischen system bei eingriffen intelligenter wesen, Z. Phys. 53, 840 (1929).
  21. R. Landauer, Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 5, 183 (1961).
  22. C. H. Bennett, The thermodynamics of computation—A review, Int. J. Theor. Phys. 21, 905 (1982).
  23. S. Lloyd, Quantum-mechanical Maxwell's demon, Phys. Rev. A 56, 3374 (1997).
  24. T. D. Kieu, The second law, Maxwell's demon, and work derivable from quantum heat engines, Phys. Rev. Lett. 93, 140403 (2004).
  25. H. T. Quan, Y. D. Wang, Y.-X. Liu, C. P. Sun, and F. Nori, Maxwell's demon assisted thermodynamic cycle in superconducting quantum circuits, Phys. Rev. Lett. 97, 180402 (2006).
  26. T. Sagawa and M. Ueda, Second law of thermodynamics with discrete quantum feedback control, Phys. Rev. Lett. 100, 080403 (2008).
  27. T. Sagawa and M. Ueda, Minimal energy cost for thermodynamic information measurement and information erasure, Phys. Rev. Lett. 102, 250602 (2009).
  28. T. Sagawa, Thermodynamics of information processing in small systems, Prog. Theor. Phys. 127, 1 (2012).
  29. D. Mandal, H. T. Quan, and C. Jarzynski, Maxwell's refrigerator: An exactly solvable model, Phys. Rev. Lett. 111, 030602 (2013).
  30. J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  31. J. Goold, M. Huber, A. Riera, L. Del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—A topical review, J. Phys. A 49, 143001 (2016).
  32. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality, Nat. Phys. 6, 988 (2010).
  33. J. V. Koski, V. F. Maisi, J. P. Pekola, and D. V. Averin, Experimental realization of a Szilard engine with a single electron, Proc. Natl. Acad. Sci. USA 111, 13786 (2014).
  34. P. A. Camati, J. P. S. Peterson, T. B. Batalhao, K. Micadei, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental rectification of entropy production by Maxwell's demon in a quantum system, Phys. Rev. Lett. 117, 240502 (2016).
  35. N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffèves, R. Azouit, P. Rouchon, and B. Huard, Observing a quantum Maxwell demon at work, Proc. Natl. Acad. Sci. USA 114, 7561 (2017).
  36. Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, and Y. Nakamura, Information-to-work conversion by Maxwell's demon in a superconducting circuit quantum electrodynamical system, Nat. Commun. 9, 1291 (2018).
  37. A. Kumar, T.-Y. Wu, F. Giraldo, and D. S. Weiss, Sorting ultracold atoms in a three-dimensional optical lattice in a realization of Maxwell's demon, Nature (London) 561, 83 (2018).
  38. K. Aggarwal, A. Rolandi, Y. Yang, J. Hickie, D. Jirovec, A. Ballabio, D. Chrastina, G. Isella, M. T. Mitchison, M. Perarnau-Llobet, et al., Rapid optimal work extraction from a quantum-dot information engine, Phys. Rev. Res. 7, L032017 (2025).
  39. A. de Oliveira Junior, J. B. Brask, and R. Chaves, A friendly guide to exorcising Maxwell's demon, PRX Quantum 6, 030201 (2025).
  40. M. Campisi, J. Pekola, and R. Fazio, Feedback-controlled heat transport in quantum devices: Theory and solid-state experimental proposal, New J. Phys. 19, 053027 (2017).
  41. To see this, use the resolution of the identity, ∑α=1KΠα=I, and the unitarity of U, implying UU†=I.
  42. S. Vaikuntanathan and C. Jarzynski, Modeling Maxwell's demon with a microcanonical Szilard engine, Phys. Rev. E 83, 061120 (2011).
  43. L. Buffoni and M. Campisi, Spontaneous fluctuation-symmetry breaking and the Landauer principle, J. Stat. Phys. 186, 31 (2022).
  44. L. Buffoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, and M. Campisi, Quantum measurement cooling, Phys. Rev. Lett. 122, 070603 (2019).
  45. A. Solfanelli, M. Falsetti, and M. Campisi, Nonadiabatic single-qubit quantum Otto engine, Phys. Rev. B 101, 054513 (2020).
  46. M. Campisi and R. Fazio, Dissipation, correlation and lags in heat engines, J. Phys. A 49, 345002 (2016).
  47. Similarly, in the case when the hybrid machine operates as a refrigerator, its cooling efficiency is bounded by the cooling Carnot efficiency [46].
  48. For simplicity here we adopt the convention that temperature is measured in units of energy, which is formally equivalent to setting Boltzmann constant kB to unity.
  49. A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004).
  50. T. Sagawa, Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics, Springer Briefs in Mathematical Physics (Springer, New York, 2020).
  51. F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43, 22 (1975).
  52. T. M. Nieuwenhuizen, Dynamics of the ideal quantum measurement of a spin-1 with a Curie-Weiss magnet, Front. Quantum Sci. Technol. 4, 1603372 (2025).
  53. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Curie-Weiss model of the quantum measurement process, Europhys. Lett. 61, 452 (2003).
  54. A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Understanding quantum measurement from the solution of dynamical models, Phys. Rep. 525, 1 (2013).
  55. L. Buffoni and M. Campisi, Cooperative quantum information erasure, Quantum 7, 961 (2023).
  56. Y. Guryanova, N. Friis, and M. Huber, Ideal projective measurements have infinite resource costs, Quantum 4, 222 (2020).
  57. P. Taranto, F. Bakhshinezhad, A. Bluhm, R. Silva, N. Friis, M. P. E. Lock, G. Vitagliano, F. C. Binder, T. Debarba, E. Schwarzhans, F. Clivaz, and M. Huber, Landauer versus Nernst: What is the true cost of cooling a quantum system? PRX Quantum 4, 010332 (2023).
  58. L. Bassman Oftelie, A. De Pasquale, and M. Campisi, Dynamic cooling on contemporary quantum computers, PRX Quantum 5, 030309 (2024).
  59. https://github.com/lebassman/Information_Engines.

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Phys. Rev. A 113, 052453– Published 26 May, 2026
  • Received 15 December 2025
  • Accepted 4 May 2026
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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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