Static and dynamical nonequilibrium fluctuations

TL;DR

This paper explores different types of fluctuations in nonequilibrium systems, analyzing their relation to entropy production and escape rates, and explains why relative entropy obeys a Hamilton-Jacobi equation.

Contribution

It provides a unified discussion of static and dynamical fluctuations in nonequilibrium systems, linking measurement methods to entropy and escape rates, and clarifies the mathematical structure of relative entropy.

Findings

Relation between measurement schemes and entropy production

Connection of fluctuations to escape rates

Relative entropy satisfies a Hamilton-Jacobi equation

Abstract

Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with escape rates. A simple explanation of why the relative entropy satisfies a Hamilton-Jacobi equation is added.