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Axiomatic relation between thermodynamic and information-theoretic entropies

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JournalPhysical Review Letters
DateAccepted/In press - 4 Nov 2016
DatePublished (current) - 22 Dec 2016
Issue number26
Volume117
Number of pages6
Original languageEnglish

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.

    Research areas

  • quant-ph, cond-mat.stat-mech

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