We elucidate the connection between the Kolmogorov-Sinai entropy rate kappa
and the time evolution of the physical or statistical entropy S. For a lar
ge family of chaotic conservative dynamical systems including the simplest
ones, the evolution of S(t) for far-from-equilibrium processes includes a s
tage during which S is a simple linear function of time whose slope is kapp
a. We present numerical confirmation of this connection for a number of cha
otic symplectic maps, ranging from the simplest two-dimensional ones to a f
our-dimensional and strongly nonlinear map. [S0031-9007(98)08099-5].