Axiomatic relation between thermodynamic and information-theoretic entropies

TL;DR

This paper establishes an axiomatic connection between thermodynamic entropy and information-theoretic entropy, including Shannon and von Neumann entropies, revealing their correspondence in equilibrium and non-equilibrium contexts.

Contribution

It introduces an axiomatic framework linking thermodynamic and information-theoretic entropies, extending the relation to quantum systems and non-equilibrium scenarios.

Findings

Clausius entropy relates directly to Shannon and von Neumann entropies.

Entropy measures in non-equilibrium thermodynamics correspond to one-shot information theory entropies.

A unified framework connects macroscopic thermodynamic and microscopic informational descriptions.

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.