Principle of Pattern Selection for Nonequilibrium Phenomena

Abstract

A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns, which characterizes multiple solutions as more or less probable with respect to each other. The most probable pattern is naturally defined by the maximum of the pattern distribution. This maximum is shown to be equivalent to the {\it minimum of local contraction}. The formulated principle plays for nonequilibrium dynamical systems the same ordering role as the condition of minimal free energy for equilibrium statistical systems. The generality of the principle is illustrated by several examples of different nature.