Irreversible spherical model and its stationary entropy production rate

TL;DR

This paper analyzes an irreversible spherical model on hypercubic lattices, deriving an explicit stationary distribution and calculating the non-zero entropy production rate caused by asymmetric transition rates.

Contribution

It provides an explicit Boltzmann-Gibbs type stationary distribution for an irreversible model, enabling exact entropy production calculations.

Findings

Stationary distribution is of Boltzmann-Gibbs type despite irreversibility

Entropy production rate is explicitly calculated and non-zero with asymmetric rates

Model extends understanding of nonequilibrium stationary states in spherical models

Abstract

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric.