Strong fluctuation theorem for nonstationary nonequilibrium systems

TL;DR

This paper derives a finite-time detailed fluctuation theorem for environmental entropy in nonstationary nonequilibrium systems, applicable to systems with constant rates and arbitrary initial conditions, with numerical validation.

Contribution

It introduces a new fluctuation theorem for environmental entropy applicable to nonstationary systems with arbitrary initial states.

Findings

The fluctuation theorem holds for systems with constant rates and arbitrary initial distributions.

Numerical tests confirm the theorem for Markov jump processes and surface growth models.

Implications for temperature quenches in classical equilibrium systems are discussed.

Abstract

We introduce a finite-time detailed fluctuation theorem for the environmental entropy of the form $\tilde P(\Delta S_{env}) = e^{\Delta S_{env}} \tilde P(-\Delta S_{env})$ for an appropriately weighted probability density of the external entropy production in the environment. The fluctuation theorem is valid for nonequilibrium systems with constant rates starting with an arbitrary initial probability distribution. We discuss the implication of this new relation for the case of a temperature quench in classical equilibrium systems. The fluctuation theorem is tested numerically for a Markov jump process with six states and for a surface growth model.