Istituto di Biofisica     
Buiatti M., Grigolini P., Palatella L. A non extensive approach to the entropy of symbolic sequences. In: Physica A-Statistical Mechanics and Its Applications, vol. 268 (1-2) pp. 214 - 224. Elsevier, 1999.
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)∝1/lμ. The numerical evaluation of the KST entropy suggests that at the value μ=2 a sort of abrupt transition might occur. For the values of μ in the range 1<μ<2 the entropic index q is expected to vanish, as a consequence of the fact that in this case the average length left angle bracketlright-pointing angle bracket diverges, thereby breaking the balance between determinism and randomness in favor of determinism. In the region μgreater-or-equal, slanted2 the entropic index q seems to depend on μ through the power law expression q=(μ−2)α with α≈0.13 (q=1 with μ>3). It is argued that this phase-transition-like property signals the onset of the thermodynamical regime at μ=2.
DOI: 10.1016/S0378-4371(99)00062-X
Subject Symbolic sequences

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