Mathematical structure derived from the q-multinomial coefficient in Tsallis statistics

Details Mathematical structure derived from the q-multinomial coefficient in Tsallis statistics Mathematical structure derived from the q-multinomial coefficient in Tsallis statistics

2004-01-27

arxiv.org/abs/cond-mat/0401546v1

Physics

Condensed Matter

Statistical Mechanics

21 pages, submitted

Scientific paper

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 $\otimes_{q}$ 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 ?"

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