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Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies

Weilenmann, Mirjam and Kraemer, Lea and Faist, Philippe and Renner, Renato (2016) Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies. Physical Review Letters, 117 (26). Art. No. 260601. ISSN 0031-9007. doi:10.1103/PhysRevLett.117.260601. https://resolver.caltech.edu/CaltechAUTHORS:20170103-134537008

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Abstract

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.117.260601DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.260601PublisherArticle
https://arxiv.org/abs/1501.06920arXivDiscussion Paper
Additional Information:© 2016 The Authors. 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. (Received 22 September 2015; revised manuscript received 4 November 2016; published 22 December 2016) This project has been supported by the Swiss National Science Foundation (SNSF) via Project Grant No. 200021_153296 and via the NCCR “QSIT,” by the European Research Council (ERC) via Project No. 258932, and by the COST Action MP1209.
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200021_153296
National Centre of Competence in Research (NCCR) QSIT – Quantum Science & TechnologyUNSPECIFIED
European Research Council (ERC)258932
COST ActionMP1209
Issue or Number:26
DOI:10.1103/PhysRevLett.117.260601
Record Number:CaltechAUTHORS:20170103-134537008
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170103-134537008
Official Citation:Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies Mirjam Weilenmann, Lea Kraemer, Philippe Faist, and Renato Renner Phys. Rev. Lett. 117, 260601
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73182
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:03 Jan 2017 21:57
Last Modified:11 Nov 2021 05:12

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