2016/11/04 by Mehmet Niyazi Çankaya, Jan Korbel · 11 citations
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Entropy (arrow of time) #Entropy rate #Joint entropy #Joint quantum entropy #Mathematics #Maximum entropy probability distribution #Maximum entropy thermodynamics #Min entropy #Physics #Principle of maximum entropy #Rényi entropy #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistical physics #Statistics #Thermodynamics #Tsallis entropy #Tsallis statistics #cond-mat.stat-mech #math-ph #math.MP #stat.AP
paper · pdf · doi:10.1016/j.physa.2017.02.009
published in Physica A Statistical Mechanics and its Applications 475, 1-10 (Elsevier BV)
arxiv created 2016/11/04 · openalex publication_date 2017/02/09 · arxiv updated 2017/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including the definition of hybrid entropy for continuous distributions, its relation to discrete entropy and calculation of hybrid entropy for some well-known distributions. Additionally, definition of hybrid divergence and its connection to Fisher metric is also discussed. Interestingly, the main properties of continuous hybrid entropy and hybrid divergence are completely different from measures based on Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy.