Lyapunov exponents, entropy production, and decoherence

We establish that the entropy production rate of a classically chaotic Hami ltonian system coupled to the environment settles, after a transient, to a metastable value given by the sum of positive generalized Lyapunov exponent s. A metastable steady state is generated in this process. This behavior al so occurs in quantum systems close to the classical limit, where it leads t o the restoration of quantum-classical correspondence in chaotic systems co upled to the environment.