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Published December 23, 2016 | Published + Supplemental Material
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Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies

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.

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.

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Published - PhysRevLett.117.260601.pdf

Supplemental Material - supplemental_material.pdf

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