On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics - Furuichi, Shigeru (Journal of mathematical physics, 2009)
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 non-negativity 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.