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arXiv · 1501.07386

On q-non-extensive statistics with non-Tsallisian entropy

Petr Jizba·Jan Korbel
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Abstract

We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the entropy thus obtained is uniquely solved in terms of a one-parameter family of information measures. The ensuing maximal-entropy distribution is phrased in terms of a special function known as the Lambert W--function. We analyze the corresponding "high" and "low-temperature" asymptotics and reveal a non-trivial structure of the parameter space.

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BibTeXRIS

Petr Jizba, Jan Korbel. 2015-01-29. On q-non-extensive statistics with non-Tsallisian entropy. https://doi.org/10.1016/j.physa.2015.10.084

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