A generalized Kolmogorov–Sinai-like entropy under Markov shifts in symbolic dynamics

Qiang Liu, Ke-Fei Cao and Shou-Li Peng

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 20, 4333-4344

Abstract: In this paper, a generalized Kolmogorov–Sinai-like entropy (KSq entropy) in the sense of Tsallis is proposed with a nonextensive parameter q under Markov shifts, which contains the classical Kolmogorov–Sinai (KS) entropy and the Rényi entropy as well as Bernoulli shifts as special cases. To verify the formula of this KSq entropy, a one-dimensional iterative system is chosen as an example of Markov shifts, and its KSq entropy is evaluated by a new refinement method of symbolic dynamics called symbolic refinement which differs from the conventional numerical method. The numerical results show that this KSq entropy is monotonically decreasing as q increases.

Keywords: Generalized Kolmogorov–Sinai-like entropy; Rényi entropy; Tsallis entropy; Markov shift; Symbolic dynamics (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:20:p:4333-4344

DOI: 10.1016/j.physa.2009.07.003

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