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arXiv · 1001.1383

On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics

Shigeru Furuichi
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Abstract

We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-expectation value and the $q$-Gaussian distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-variance, as applications of the nonnegativity of the Tsallis relative entropy, without using the Lagrange multipliers method. In addition, we define a $q$-Fisher information and then prove a $q$-Cramér-Rao inequality that the $q$-Gaussian distribution with special $q$-variances attains the minimum value of the $q$-Fisher information.

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Shigeru Furuichi. 2010-01-08. On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics. https://doi.org/10.1063/1.3063640

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