Microscopic Chaos and Nonequilibrium Statistical Mechanics: From Quantum to Classical Dynamics

We review recent results on the relationships between the microscopic chaos in the motion of atoms or molecules in fluids and the transport properties sustained across these macroscopic systems. In the escape-rate formalism, the transport coefficients can be expressed in terms of the positive Lyapunov exponents, the Kolmogorov-Sinai entropy per unit time or the Hausdorff dimension of a fractal repeller generated in the phase space by the nonequilibrium constraints. In the same context, nonequilibrium steady states turn out to be described by singular invariant measures in the large-system limit. This singular character of the nonequilibrium measures explains the entropy production expected from irreversible thermodynamics. Moreover, we also discuss how the aforementioned classical and kinetic properties can emerge out of the wave dynamics in quantum systems.