Geometrical Expression of Excess Entropy Production

TL;DR

This paper presents a geometric framework for quantifying excess entropy production during quasi-static transitions between nonequilibrium steady states in Markovian jump processes, highlighting the role of trajectory-dependent vector potentials.

Contribution

It introduces an exact, geometrical expression for excess entropy production applicable to nonlinear and nonequilibrium systems, analogous to the Berry phase.

Findings

Excess entropy production depends solely on the trajectory in parameter space.

Vector potentials are essential for developing thermodynamics of nonequilibrium steady states.

The expression is applicable to nonlinear and nonequilibrium situations.

Abstract

We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct thermodynamics of nonequilibrium steady states.