2004/01/27 by Hiroki Suyari, Suyari, Hiroki
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0401546
21 pages, submitted
arxiv created 2004/01/27 · openalex publication_date 2004/01/27 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We present the conclusive mathematical structure behind Tsallis statistics. We obtain mainly the following five theoretical results: (i) the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy, (ii) symmetry behind Tsallis statistics, (iii) the numerical computations revealing the existence of the central limit theorem in Tsallis statistics, (iv) Pascal's triangle in Tsallis statistics and its properties, (v) the self-similarity of the q-product ⊗q leading to successful applications in Tsallis statistics. In particular, the third result (iii) provides us with a mathematical representation of a convincible answer to the physical problem: "Why so many power-law behaviors exist in nature universally ?"