The non-extensive version of the Kolmogorov-Sinai entropy at work

Details The non-extensive version of the Kolmogorov-Sinai entropy at work The non-extensive version of the Kolmogorov-Sinai entropy at work

1999-11-25

arxiv.org/abs/cond-mat/9911412v1

Physics

Condensed Matter

4 pages, 3 figures, submitted to PRL

Scientific paper

We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power law rather than exponential sensitivity to initial conditions. The computer treatment is made difficult, if not impossible, by the multifractal nature of the natural invariant distribution: Thus the statistical average is carried out on the power index. The resulting entropy time evolution becomes a smooth and linear function of time with the non-extensive index Q < 1 prescribed by the heuristic arguments of earlier work, thereby showing how to make the correct entropic prediction in the spirit of the single-trajectory approach of Kolmogorov.

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