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Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for<i>q</i>-exponential distributions
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis …