Entropy production rate of nonequilibrium systems from the Fokker-Planck equation

TL;DR

This paper develops a new method to calculate the entropy production rate in nonequilibrium systems using the Fokker-Planck equation, providing a more practical expression and demonstrating its application.

Contribution

It introduces a novel way to derive the transition rate from the Fokker-Planck equation for entropy production calculation, improving practicality.

Findings

Derived a new expression for entropy production rate

Applied the method to specific examples

Enhanced the calculation efficiency for nonequilibrium systems

Abstract

The entropy production rate of nonequilibrium systems is studied via the Fokker-Planck equation. This approach, based on the entropy production rate equation given by Schnakenberg from a master equation, requires information of the transition rate of the system under study. We obtain the transition rate from the conditional probability extracted from the Fokker-Planck equation and then derive a new and more operable expression for the entropy production rate. Examples are presented as applications of our approach.