ENTROPY PRODUCTION IN NONEQUILIBRIUM STATISTICAL-MECHANICS

We consider systems of nonequilibrium statistical mechanics, driven by nonconservative forces and in contact with an ideal thermostat. These are smooth dynamical systems for which one can define natural station ary states mu (SRB in the simplest case) and entropy production e(mu) (minus the sum of the Lyapunov exponents in the simplest case). We giv e exact and explicit definitions of the entropy production e(mu) for t he various situations of physical interest. We prove that e(mu) greate r than or equal to 0 and indicate cases where e(mu) > 0. The novelty o f the approach is that we do not try to compute entropy production dir ectly, but make it depend on the identification oi a natural stationar y state for the system.