Entropy variation and Lyapunov exponents of a nonequilibrium system

Abstract

A macroscopic state space is introduced to describe macro-states of a nonequilibrium system. The space is spanned by averages of basic variables of the system. The entropy variation rate of the system is derived as average trace of an entropy source matrix which is a term in a memory matrix of the system. The entropy variation and Lyapunov exponents are shown determined by the non-uniformity in time and in the macro-state space of fluctuation force associated with each variable of the system. This indicates a fundamental relationship between fluctuations and dissipation. It is shown that for an ergodic system, the sum of Lyapunov exponents is equal to the time-rate of information entropy or average trace of the entropy source matrix. The study is illustrated by a simple fluid.