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

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