Relations between Dissipated Work and R\'enyi Divergences

TL;DR

This paper establishes a universal relation linking dissipated work in non-equilibrium thermodynamics to Rényi divergences from information theory, applicable to classical and quantum systems far from equilibrium.

Contribution

It introduces a general relation connecting dissipated work and Rényi divergences, extending thermodynamics and information theory insights to arbitrary far-from-equilibrium processes.

Findings

The generating function of dissipated work relates to Rényi divergences.

The relation applies universally to classical and quantum systems.

It leverages time reversal symmetry in driven processes.

Abstract

In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the R\'{e}nyi divergences, a fundamental concept in information theory. Specifically, we find that the generating function of the dissipated work under an arbitrary time-dependent driving process is related to the R\'{e}nyi divergences between a non-equilibrium state in the driven process and a non-equilibrium state in its time reversed process. This relation is a consequence of time reversal symmetry in driven process and is universally applicable to both finite classical system and finite quantum system, arbitrarily far from equilibrium.