Universal Property of the Housekeeping Entropy Production

TL;DR

This paper proves that the distribution of housekeeping entropy production in nonequilibrium systems is universally Gaussian, regardless of system specifics or state, and introduces a stochastic differential equation for it.

Contribution

The authors derive a Langevin-type equation for housekeeping entropy production and establish its universal Gaussian distribution across diverse nonequilibrium systems.

Findings

Housekeeping entropy production follows a Gaussian distribution.

The distribution's universality holds for steady and transient states.

Numerical simulations confirm the theoretical predictions.

Abstract

The entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative. Among the total entropy production, the housekeeping entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state. We derive a Langevin-type stochastic differential equation for the housekeeping entropy production. The equation allows us to define a housekeeping entropic time $\tau$. Remarkably, it turns out that the probability distribution of the housekeeping entropy production at a fixed value of $\tau$ is given by the Gaussian distribution regardless of system details. The Gaussian distribution is universal for any systems, whether in the steady state or in the transient state, whether they are driven by time-independent or time-dependent driving forces. We demonstrate the universal distribution numerically for model systems.