Nonequilibrium thermodynamics as a gauge theory

TL;DR

This paper formulates nonequilibrium thermodynamics within a gauge theory framework, revealing that entropy production and irreversibility have geometric and gauge-invariant interpretations, linking thermodynamics to gauge symmetry and information theory.

Contribution

It introduces a gauge-theoretic approach to nonequilibrium thermodynamics, interpreting entropy production as a gauge-invariant quantity and relating irreversibility to geometric phases.

Findings

Entropy production arises as a gauge-invariant quantity.

Clausius's measure of irreversibility is a geometric phase.

Transition rates relate to locally-detailed-balanced heat reservoirs.

Abstract

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.