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

In this paper, a generalized Kolmogorov–Sinai-like entropy (KSq entropy) in the sense of Tsallis is proposed with a nonextensive parameter qq 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 qq increases.