2009/01/01 by Shigeru Furuichi · 41 citations
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Applied mathematics #Binary entropy function #Entropy (arrow of time) #Fisher information #Gaussian #Information theory #Lagrange multiplier #Mathematical optimization #Mathematics #Maximum entropy probability distribution #Maximum entropy thermodynamics #Physics #Principle of maximum entropy #Quantum mechanics #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistical physics #Statistics #Tsallis entropy #Tsallis statistics #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.3063640
published in Journal of Mathematical Physics 50(1) (American Institute of Physics)
openalex publication_date 2009/01/01 · arxiv created 2010/01/08 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.