Phase Transition and Slowing Down in Non-Equilibrium Stochastic Processes

Abstract

A general criterion of appearance of slowing down in non-equilibrium stochastic processes is proposed. Many examples for this general criterion are shown, in which a phenomenon of slowing down occurs at a certain value of the relevant parameter. In particular, a generalized scaling treatment of transient phenomena is effectively applied to deriving the relaxation spectra of some multiplicative stochastic processes. The concept of asymptotic slowing down for finite systems is also proposed.