On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics
arXiv:1001.1383 · doi:10.1063/1.3063640
Abstract
We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the -canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the -expectation value and the -Gaussian distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the -variance, as applications of the nonnegativity of the Tsallis relative entropy, without using the Lagrange multipliers method. In addition, we define a -Fisher information and then prove a -Cramér-Rao inequality that the -Gaussian distribution with special -variances attains the minimum value of the -Fisher information.
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