Axiomatic relation between thermodynamic and information-theoretic entropies

Mirjam Weilenmann; Lea Krämer; Philippe Faist; Renato Renner

doi:10.1103/PhysRevLett.117.260601

Axiomatic relation between thermodynamic and information-theoretic entropies

Mirjam Weilenmann, Lea Krämer, Philippe Faist, Renato Renner

Mathematics

Research output: Contribution to journal › Article › peer-review

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 [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.

Original language	English
Article number	260601
Number of pages	6
Journal	Physical Review Letters
Volume	117
Issue number	26
DOIs	https://doi.org/10.1103/PhysRevLett.117.260601
Publication status	Published - 22 Dec 2016

Keywords

quant-ph
cond-mat.stat-mech

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10.1103/PhysRevLett.117.260601

PhysRevLett.117.260601Final published version, 166 KBLicence: CC BY

Cite this

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AB - 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 [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory.

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