Minimum entropy production principle from a dynamical fluctuation law

TL;DR

This paper links the minimum entropy production principle to dynamical fluctuation theory in Markov processes, explaining its approximate nature near equilibrium and addressing complexities in systems with sign-changing degrees of freedom.

Contribution

It identifies the entropy production as a large deviation rate function for Markov process fluctuations, providing a theoretical foundation for the principle's validity near equilibrium.

Findings

Entropy production corresponds to the large deviation rate function.

The principle is derived from the structure of dynamical fluctuations.

Subtleties arise when degrees of freedom change sign under time-reversal.

Abstract

The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical distribution of occupation times for a class of Markov processes, we identify the entropy production as the large deviation rate function, up to leading order when expanding around a detailed balance dynamics. In that way, the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations, and its approximate character gets an explanation. We also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time-reversal.