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

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.

9 pages, 7 figures

References in corpus (3)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Evaporation/condensation transition of the two dimensional Potts model in microcanonical ensemble
• Nonequilibrium critical relaxations of the order parameter and energy in the two-dimensional ferromagnetic Potts model