title: 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.
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland.|Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom.
authors.forename: Mirjam
authors.initials: M
authors.lastname: Weilenmann
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland.
authors.forename: Lea
authors.initials: L
authors.lastname: Kraemer
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland.|Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Philippe
authors.initials: P
authors.lastname: Faist
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland.
authors.forename: Renato
authors.initials: R
authors.lastname: Renner