Kolmogorov-Sinai Entropy Rate versus Physical Entropy

We elucidate the connection between the Kolmogorov-Sinai entropy rate κ and the time evolution of the physical or statistical entropy S. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution of $S(t)$ for far-from-equilibrium processes includes a stage during which S is a simple linear function of time whose slope is κ. We present numerical confirmation of this connection for a number of chaotic symplectic maps, ranging from the simplest two-dimensional ones to a four-dimensional and strongly nonlinear map.