Lyapunov Exponents, Entropy Production, and Decoherence

We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a metastable value given by the sum of positive generalized Lyapunov exponents. A metastable steady state is generated in this process. This behavior also occurs in quantum systems close to the classical limit, where it leads to the restoration of quantum-classical correspondence in chaotic systems coupled to the environment.