Symbolic sequences with long-range correlations an expected to result in a
slow regression to a steady state of entropy increase. However, we prove th
at also in this case a fast transition to a constant rate of entropy increa
se can be obtained, provided that the extensive entropy of Tsallis with ent
ropic index q is adopted, thereby resulting in a new form of entropy that w
e 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) a 1/l(mu). The numerical evaluation of t
he KST entropy suggests that at the value mu = 2 a sort of abrupt transitio
n might occur. For the values of mu in the range 1 < mu < 2 the cntropic in
dex 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 dete
rminism and randomness in favor of determinism. In the region mu greater th
an or equal to 2 the entropic index q seems to depend on mu through the pow
er law expression q = (mu - 2)(alpha) with alpha approximate to 0.13 (q = 1
with mu > 3). It is argued that this phase-transition-like property signal
s the onset of the thermodynamical regime at mu = 2. (C) 1999 Elsevier Scie
nce B.V. All rights reserved.