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Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

Faist, Philippe and Sagawa, Takahiro and Kato, Kohtaro and Nagaoka, Hiroshi and Brandão, Fernando G. S. L. (2019) Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems. Physical Review Letters, 123 (25). Art. No. 250601. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20190801-134555157

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Abstract

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein’s lemma for ergodic states and local Gibbs states. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.123.250601DOIArticle
https://arxiv.org/abs/1907.05651arXivDiscussion Paper
ORCID:
AuthorORCID
Kato, Kohtaro0000-0003-3317-2004
Nagaoka, Hiroshi0000-0002-0085-2794
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2019 American Physical Society. Received 8 August 2019; published 17 December 2019. The authors are grateful to Matteo Lostaglio, Keiji Matsumoto, Yoshiko Ogata, David Sutter, and Hiroyasu Tajima for valuable discussions. T. S. is supported by JSPS KAKENHI Grants No. JP16H02211 and No. JP19H05796. P. F. is supported by the Institute for Quantum Information and Matter (IQIM) at Caltech which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant No. PHY-1733907), by the Department of Energy Award No. DE-SC0018407, by the Swiss National Science Foundation (SNSF) via the NCCR QSIT and via Project No. 200020_16584, and by the Deutsche Forschungsgemeinschaft (DFG) Research Unit FOR 2724. K. K. acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1733907). F. B. is supported by the NSF.
Group:UNSPECIFIED, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)JP16H02211
Japan Society for the Promotion of Science (JSPS)JP19H05796
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
Department of Energy (DOE)DE-SC0018407
Swiss National Science Foundation (SNSF)200020_16584
Deutsche Forschungsgemeinschaft (DFG)FOR 2724
Issue or Number:25
Record Number:CaltechAUTHORS:20190801-134555157
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190801-134555157
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97605
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Aug 2019 21:30
Last Modified:04 Jun 2020 10:14

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