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

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

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.

Suggested Citation

  • Liu, Qiang & Cao, Ke-Fei & Peng, Shou-Li, 2009. "A generalized Kolmogorov–Sinai-like entropy under Markov shifts in symbolic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4333-4344.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:20:p:4333-4344
    DOI: 10.1016/j.physa.2009.07.003
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