  Under certain conditions, the rate of increase of the statistical entropy of
a simple, fully chaotic, conservative system is known to be given by a single
number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This
connection is here generalized to a simple dissipative system, the logistic
map, and especially to the chaos threshold of the latter, the edge of chaos. It
is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon
entropy is not appropriate. Instead, the non-extensive entropy $S_q\equiv
\frac{1-\sum_{i=1}^W p_i^q}{q-1}$, must be used. The latter contains a
parameter q, the entropic index which must be given a special value $q^*\ne 1$
(for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos
under consideration. The same q^* enters also in the description of the
sensitivity to initial conditions, as well as in that of the multifractal
spectrum of the attractor.
