  We consider several low--dimensional chaotic maps started in
far-from-equilibrium initial conditions and we study the process of relaxation
to equilibrium. In the case of conservative maps the Boltzmann-Gibbs entropy
S(t) increases linearly in time with a slope equal to the Kolmogorov-Sinai
entropy rate. The same result is obtained also for a simple case of dissipative
system, the logistic map, when considered in the chaotic regime. A very
interesting results is found at the chaos threshold. In this case, the usual
Boltzmann-Gibbs is not appropriate and in order to have a linear increase, as
for the chaotic case, we need to use the generalized q-dependent Tsallis
entropy $S_q(t)$ with a particular value of a q different from 1 (when q=1 the
generalized entropy reduces to the Boltzmann-Gibbs). The entropic index q
appears to be characteristic of the dynamical system.
