Entropy production of the contact model

TL;DR

This paper introduces a new entropy production formula for stochastic systems with asymmetric transition rates, applies it to the contact process, and finds critical behavior at phase transitions.

Contribution

It presents a novel entropy production expression suitable for systems with zero reverse transition rates and applies it to analyze the contact process.

Findings

Entropy production rate is finite at the stationary state.

A singularity with diverging slope occurs at the critical point.

The entropy flux is linear in the probability distribution.

Abstract

We propose an expression for the production of entropy for system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive defined and based on the inequality $x\ln x-(x-1)\ge0$. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.