2005/01/31 by Ambedkar Dukkipati, M. Narasimha Murty, Shalabh Bhatnagar
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Entropy (arrow of time) #Generalized relative entropy #Kullback–Leibler divergence #Mathematical Inequalities and Applications #Mathematical optimization #Mathematics #Maximum entropy probability distribution #Minification #Physics #Principle of maximum entropy #Quantum mechanics #Quantum relative entropy #Statistical Mechanics and Entropy #Statistical physics #Statistics #Thermodynamics #Tsallis entropy #Tsallis statistics #math-ph #math.MP
paper · pdf · doi:10.1016/j.physa.2005.06.072
published as Physica A 361 (2006) 124-138 · 15 pages, change of title, revision of triangle equality
arxiv created 2005/03/22 · openalex publication_date 2005/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Kullback-Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one parameter generalization of Kullback-Leibler relative-entropy in the nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classical case. In the representation of such a minimum relative-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced to derive the mathematical structure behind the Tsallis statistics. One of our main results is generalization of triangle equality of relative-entropy minimization to the nonextensive case.