On the Fokker–Planck approach to the stochastic thermodynamics of reactive systems

Abstract

Stochastic thermodynamics is an extension of classical nonequilibrium thermodynamics that aims at including the effect of fluctuations occurring at small scales. In many cases, the starting point of such approaches is a Fokker–Planck equation for the probability density associated to the underlying stochastic variables. It is known that for chemically reactive systems, the usual equation for entropy production derived in this framework is not consistent with its macroscopic counterpart. It moreover also differs from the expression obtained with the master equation, from which the aforementioned Fokker–Planck equation derives. In the present work, we obtain a Fokker–Planck based alternative formula for entropy production in reactive systems that converges to the correct expression in the thermodynamic limit and is moreover consistent with expressions obtained with the master-equation based approach.