Kolmogorov-Sinai entropy rate versus physical entropy

We elucidate the connection between the Kolmogorov-Sinai entropy rate kappa 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 kappa. 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. [S0031-9007(98)08099-5].