[en] The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.
Disciplines :
Physique
Auteur, co-auteur :
PTASZYNSKI, Krzysztof ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
ESPOSITO, Massimiliano ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Ensemble dependence of information-theoretic contributions to the entropy production.
Narodowe Centrum Nauki Ministerstwo Edukacji i Nauki Foundational Questions Institute
Subventionnement (détails) :
K.P. has been supported by the National Science Centre, Poland, under Project No. 2017/27/N/ST3/01604, and by the Scholarships of Minister of Science and Higher Education. This research was also supported by the FQXi foundation Project No. FQXi-IAF19-05-52 Colloids and superconducting quantum circuits.
A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011) 0034-6861 10.1103/RevModPhys.83.863.
J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many-body systems out of equilibrium, Nat. Phys. 11, 124 (2015) 1745-2473 10.1038/nphys3215.
C. Gogolin and J. Eisert, Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016) 0034-4885 10.1088/0034-4885/79/5/056001.
L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016) 0001-8732 10.1080/00018732.2016.1198134.
T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Thermalization and prethermalization in isolated quantum systems: A theoretical overview, J. Phys. B: At. Mol. Opt. Phys. 51, 112001 (2018) 0953-4075 10.1088/1361-6455/aabcdf.
H. Spohn, Entropy production for quantum dynamical semigroups, J. Math. Phys. 19, 1227 (1978) 0022-2488 10.1063/1.523789.
D. Andrieux, P. Gaspard, T. Monnai, and S. Tasaki, The fluctuation theorem for currents in open quantum systems, New J. Phys. 11, 043014 (2009) 1367-2630 10.1088/1367-2630/11/4/043014.
M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009) 0034-6861 10.1103/RevModPhys.81.1665.
C. Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Annu. Rev. Condens. Matter Phys. 2, 329 (2011) 1947-5454 10.1146/annurev-conmatphys-062910-140506.
M. Campisi, P. Hänggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011) 0034-6861 10.1103/RevModPhys.83.771.
M. Campisi and P. Hänggi, Fluctuation, dissipation and the arrow of time, Entropy 13, 2024 (2011) 1099-4300 10.3390/e13122024.
M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013) 2041-1723 10.1038/ncomms3059.
F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Resource Theory of Quantum States Out of Thermal Equilibrium, Phys. Rev. Lett. 111, 250404 (2013) 0031-9007 10.1103/PhysRevLett.111.250404.
F. G. S. L. Brandão, M. Horodecki, N. H. Y. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynamics, Proc. Natl. Acad. Sci. USA 112, 3275 (2015) 0027-8424 10.1073/pnas.1411728112.
P. Strasberg and M. Esposito, Non-Markovianity and negative entropy production rates, Phys. Rev. E 99, 012120 (2019) 2470-0045 10.1103/PhysRevE.99.012120.
Á. Rivas, Strong Coupling Thermodynamics of Open Quantum Systems, Phys. Rev. Lett. 124, 160601 (2020) 0031-9007 10.1103/PhysRevLett.124.160601.
P. Strasberg and A. Winter, First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy, PRX Quantum 2, 030202 (2021) 2691-3399 10.1103/PRXQuantum.2.030202.
G. T. Landi and M. Paternostro, Irreversible entropy production: From classical to quantum, Rev. Mod. Phys. 93, 035008 (2021) 0034-6861 10.1103/RevModPhys.93.035008.
M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010) 1367-2630 10.1088/1367-2630/12/1/013013.
P. Strasberg, M. G. Díaz, and A. Riera-Campeny, Clausius inequality for finite baths reveals universal efficiency improvements, Phys. Rev. E 104, L022103 (2021) 2470-0045 10.1103/PhysRevE.104.L022103.
K. Ptaszyński and M. Esposito, Entropy Production in Open Systems: The Predominant Role of Intraenvironment Correlations, Phys. Rev. Lett. 123, 200603 (2019) 0031-9007 10.1103/PhysRevLett.123.200603.
A. Colla and H.-P. Breuer, Entropy production and the role of correlations in quantum Brownian motion, Phys. Rev. A 104, 052408 (2021) 2469-9926 10.1103/PhysRevA.104.052408.
M. Esposito and P. Gaspard, Spin relaxation in a complex environment, Phys. Rev. E 68, 066113 (2003) 1063-651X 10.1103/PhysRevE.68.066113.
M. Esposito and P. Gaspard, Quantum master equation for the microcanonical ensemble, Phys. Rev. E 76, 041134 (2007) 1539-3755 10.1103/PhysRevE.76.041134.
A. Riera-Campeny, A. Sanpera, and P. Strasberg, Quantum systems correlated with a finite bath: Nonequilibrium dynamics and thermodynamics, PRX Quantum 2, 010340 (2021) 2691-3399 10.1103/PRXQuantum.2.010340.
R. Heveling, J. Wang, R. Steinigeweg, and J. Gemmer, Integral fluctuation theorem and generalized Clausius inequality for microcanonical and pure states, Phys. Rev. E 105, 064112 (2022) 2470-0045 10.1103/PhysRevE.105.064112.
J. W. Gibbs, Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics (C. Scribner's Sons, New York, 1902).
H. Touchette, Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels, J. Stat. Phys. 159, 987 (2015) 0022-4715 10.1007/s10955-015-1212-2.
A. O. Caldeira and A. J. Leggett, Quantum tunneling in a dissipative system, Ann. Phys. 149, 374 (1983) 0003-4916 10.1016/0003-4916(83)90202-6.
J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991) 1050-2947 10.1103/PhysRevA.43.2046.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994) 1063-651X 10.1103/PhysRevE.50.888.
J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys. 81, 082001 (2018) 0034-4885 10.1088/1361-6633/aac9f1.
E. Iyoda, K. Kaneko, and T. Sagawa, Fluctuation Theorem for Many-Body Pure Quantum States, Phys. Rev. Lett. 119, 100601 (2017) 0031-9007 10.1103/PhysRevLett.119.100601.
E. Iyoda, K. Kaneko, and T. Sagawa, Eigenstate fluctuation theorem in the short-and long-time regimes, Phys. Rev. E 105, 044106 (2022) 2470-0045 10.1103/PhysRevE.105.044106.
H. Tasaki, From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example, Phys. Rev. Lett. 80, 1373 (1998) 0031-9007 10.1103/PhysRevLett.80.1373.
S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical typicality, Phys. Rev. Lett. 96, 050403 (2006) 0031-9007 10.1103/PhysRevLett.96.050403.
S. Camalet, Thermalisation by a boson bath in a pure state, Eur. Phys. J. B 61, 193 (2008) 1434-6028 10.1140/epjb/e2008-00065-5.
L. Dabelow, P. Vorndamme, and P. Reimann, Thermalization of locally perturbed many-body quantum systems, Phys. Rev. B 105, 024310 (2022) 2469-9950 10.1103/PhysRevB.105.024310.
W. Israel, Thermo-field dynamics of black holes, Phys. Lett. A 57, 107 (1976) 0375-9601 10.1016/0375-9601(76)90178-X.
S. Sugiura and A. Shimizu, Canonical Thermal Pure Quantum State, Phys. Rev. Lett. 111, 010401 (2013) 0031-9007 10.1103/PhysRevLett.111.010401.
H. Endo, C. Hotta, and A. Shimizu, From Linear to Nonlinear Responses of Thermal Pure Quantum States, Phys. Rev. Lett. 121, 220601 (2018) 0031-9007 10.1103/PhysRevLett.121.220601.
T. Heitmann, J. Richter, D. Schubert, and R. Steinigeweg, Selected applications of typicality to real-time dynamics of quantum many-body systems, Z. Naturforsch. A 75, 421 (2020) 1865-7109 10.1515/zna-2020-0010.
S. Popescu, A. J. Short, and A. Winter, Entanglement and the foundations of statistical mechanics, Nat. Phys. 2, 754 (2006) 10.1038/nphys444.
A. Smirne, N. Megier, and B. Vacchini, On the connection between microscopic description and memory effects in open quantum system dynamics, Quantum 5, 439 (2021) 2521-327X 10.22331/q-2021-04-26-439.
M. Lecar and J. Katz, The stability of the grand microcanonical ensemble for bounded isothermal spheres, Astrophys. J. 243, 983 (1981) 0004-637X 10.1086/158662.
P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, and K. Rzążewski, Fourth Statistical Ensemble for the Bose-Einstein Condensate, Phys. Rev. Lett. 79, 1789 (1997) 0031-9007 10.1103/PhysRevLett.79.1789.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.107.L052102 for numerical simulations of the noninteracting resonant level model with random pure initial states of the bath.
I. Peschel, Calculation of reduced density matrices from correlation functions, J. Phys. A: Math. Gen. 36, L205 (2003) 0305-4470 10.1088/0305-4470/36/14/101.
H. Araki and E. H. Lieb, Entropy inequalities, Commun. Math. Phys. 18, 160 (1970) 0010-3616 10.1007/BF01646092.
G. Yoo, S.-S. B. Lee, and H.-S. Sim, Detecting Kondo Entanglement by Electron Conductance, Phys. Rev. Lett. 120, 146801 (2018) 0031-9007 10.1103/PhysRevLett.120.146801.
D. Kim, J. Shim, and H.-S. Sim, Universal Thermal Entanglement of Multichannel Kondo Effects, Phys. Rev. Lett. 127, 226801 (2021) 0031-9007 10.1103/PhysRevLett.127.226801.
J. Bauer, C. Salomon, and E. Demler, Realizing a Kondo-Correlated State with Ultracold Atoms, Phys. Rev. Lett. 111, 215304 (2013) 0031-9007 10.1103/PhysRevLett.111.215304.
