Entropy production, information gain and Lyapunov exponents of random hyperbolic dynamical systems

Abstract

In this paper we introduce the concept of specific information gain ( or specific relative entropy) for random subshifts of finite type and random dynamical systems generated by small diffeomorphism-type perturbations of an Axiom-A basic set of a deterministic diffeomorphism. With this notion, we discuss in this special situation of random hyperbolic dynamical systems the measure-theoretic basis of the definition of the entropy production rate proposed by Ruelle for general random dynamical systems.