Axiomatic relation between thermodynamic and information-theoretic entropies

Mirjam Weilenmann, Lea Krämer, Philippe Faist, Renato Renner

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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 languageEnglish
Article number260601
Number of pages6
JournalPhysical Review Letters
Issue number26
Publication statusPublished - 22 Dec 2016


  • quant-ph
  • cond-mat.stat-mech

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