Usefulness of an equal-probability assumption for out-of-equilibrium states: a master equation approach

TL;DR

This paper investigates the validity of assuming equal probability for states far from equilibrium by developing a master equation approach and applying it to the critical relaxation of the 2D Potts model, showing improved dynamic predictions.

Contribution

It introduces a method to construct a master equation for nonequilibrium states based on the equal probability assumption for microscopic configurations with the same extensive variables.

Findings

Single-variable description is insufficient for nonequilibrium dynamics.

Two-variable description accurately reproduces relaxation dynamics.

Equal probability assumption can extend to some nonequilibrium states.

Abstract

We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing non-stationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena.