A non extensive approach to the entropy of symbolic sequences

Details A non extensive approach to the entropy of symbolic sequences A non extensive approach to the entropy of symbolic sequences

1999-02-06

arxiv.org/abs/chao-dyn/9902006v2

Nonlinear Sciences

Chaotic Dynamics

7 pages, revtex, 3 ps figures, to be published in Physica A, minor content changes (mostly in the conclusions) added to the pr

Scientific paper

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 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.

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