Entropy Production and Information Gain¶in Axiom-A Systems

Anosov systems are mathematical models for chaotic systems in statistical mechanics and fluid dynamics. Most of these systems enjoy the property of positive entropy production. We introduce the concept of specific information gain (or specific relative entropy) h(μ+,μ−) in Anosov systems and prove that it is identical to the entropy production rate e p (μ+) defined by Ruelle and Gallavotti in Anosov systems. From this point of view, the entropy production rate e p (μ+ characterizes the degree of macroscopic irreversibility of the system.