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arXiv · 0704.2814

A Revised Generalized Kolmogorov-Sinai-like Entropy and Markov Shifts

Qiang Liu·Shou-Li Peng
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Abstract

The Kolmogorov-Sinai entropy in the sense of Tsallis under Bernoulli shifts was obtained by Meson and Vericat [J. Math. Phys. 37, 4480(1996)]. In this paper, we propose a revised generalized Kolmogorov-Sinai-q entropy under Markov shifts. The form of this generalized entropy with factor q is nonextensive. The new generalized entropy contains the classical Kolmogorov-Sinai entropy and Renyi entropy as well as Bernoulli shifts as special cases. Applying the generalized entropy we discuss its approximate behavior qualitatively, the entropy rate and the sensitive value q^* of the nonextensive parameter q, which may exit in the interval (-2,2) nearby where the generalized entropy return to the classical K-S entropy.

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Qiang Liu, Shou-Li Peng. 2007-04-21. A Revised Generalized Kolmogorov-Sinai-like Entropy and Markov Shifts. https://arxiv.org/abs/0704.2814

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