  Symbolic sequences with long-range correlations are expected to result in a
slow regression to a steady state of entropy increase. However, we prove that
also in this case a fast transition to a constant rate of entropy increase can
be obtained, provided that the extensive entropy of Tsallis with entropic index
q is adopted, thereby resulting in a new form of entropy that we shall refer to
as Kolmogorov-Sinai-Tsallis (KST) entropy. We assume that the same symbols,
either 1 or -1, are repeated in strings of length l, with the probability
distribution p(l) proportional to 1/(l^mu). The numerical evaluation of the KST
entropy suggests that at the value mu = 2 a sort of abrupt transition might
occur. For the values of mu in the range 1<mu<2 the entropic index q is
expected to vanish, as a consequence of the fact that in this case the average
length <l> diverges, thereby breaking the balance between determinism and
randomness in favor of determinism. In the region mu > 2 the entropic index q
seems to depend on mu through the power law expression q = (mu-2)^(alpha) with
alpha approximately 0.13 (q = 1 with mu > 3). It is argued that this
phase-transition like property signals the onset of the thermodynamical regime
at mu = 2.
