1205.3349 (Tomoaki Nogawa et al.)

Usefulness of equal a priori probability assumption for
out-of-equilibrium states: a master equation approach    [PDF]

Tomoaki Nogawa, Nobuyasu Ito, Hiroshi Watanabe

We examine the effectivity of assuming equal a priori probability for out-of-equilibrium states. For this aim, we propose a method to construct a master equation in the phase space of extensive variables describing nonequilibrium (non-stationary) dynamics. The key point of the method is the assumption that the transient states are equivalent to the equilibrium (stationary) state having the same extensive variables, i.e., the principle of equal a priori probability holds for transient states. We demonstrate an application to the critical relaxation of the two dimensional Potts model with a help of Monte-Carlo simulations. While one-variable description, which is adequate for equilibrium, yields too fast relaxation dynamics, redundant two-variable description reproduces the true dynamics quantitatively well. These results suggest that some class of non-stationary state can be described with small extension of degrees of freedom, which possibly leads to a new way to understand nonequilibrium phenomena.

View original: http://arxiv.org/abs/1205.3349