Entropy production for asymmetric diffusion of particles

TL;DR

This paper investigates a non-equilibrium asymmetric diffusion process with particle creation and annihilation, deriving exact and approximate expressions for entropy production and flux, revealing their dependence on particle current and transition rate asymmetry.

Contribution

The study provides exact solutions for entropy production in a non-equilibrium exclusion process with asymmetric hopping and particle creation/annihilation, including a pair approximation analysis for the general case.

Findings

Entropy production rate is a bilinear form in particle current and log rate ratio.

Exact entropy and flux expressions are derived for specific conditions.

Stationary entropy production depends on system asymmetry and particle flux.

Abstract

We analyse a non-equilibrium exclusion process in which particles are created and annihilated in pairs and hop to the the right or to the left with different transition rates, $p$ and $q$, respectively. We have studied the dynamics of a single particle, and exactly determined the entropy, entropy production rate and entropy flux as functions of time. In the system of many particles, we have characterised the system by its probability distribution, as well as the entropy production rate in close forms, provided that $p+q$ equals the sum of dimers creation and annihilation rates. The general case, where this constraint is absent, was considered at pair approximation level; the time-dependent behaviour of the system was analysed, and the stationary entropy production was determined. In all cases, in the stationary regime, we showed that the entropy production rate is a bilinear form in the current of particles and the force $\ln(p/q)$.