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

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

2010-01-08

arxiv.org/abs/1001.1383v1

Journal of Mathematical Physics,Vol.50(2009),013303

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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 $q$-Cram\'er-Rao inequality that the $q$-Gaussian distribution with special $q$-variances attains the minimum value of the $q$-Fisher information.

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