The Steady State Distribution of the Master Equation

TL;DR

This paper investigates the steady state solutions of the master equation, providing exact and near-equilibrium expressions that align with recent developments in steady state thermodynamics.

Contribution

It introduces two new expressions for the steady state distribution of the master equation, enhancing understanding of non-equilibrium statistical mechanics.

Findings

Exact steady state distribution derived

Near-equilibrium approximation developed

Consistency with steady state thermodynamics established

Abstract

The steady states of the master equation are investigated. We give two expressions for the steady state distribution of the master equation a la the Zubarev-McLennan steady state distribution, i.e., the exact expression and an expression near equilibrium. The latter expression obtained is consistent with recent attempt of constructing steady state theormodynamics.