  We consider nonequilibrium probabilistic dynamics in logistic-like maps
$x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many
initial conditions within one among $W>>1$ intervals partitioning the phase
space and focus on the unique value $q_{sen}<1$ for which the entropic form
$S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with
time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like
$t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size
scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This
establishes quantitatively, for the first time, a long pursued relation between
sensitivity to the initial conditions and relaxation, concepts which play
central roles in nonextensive statistical mechanics.
