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

Petr Jizba and Jan Korbel

Physica A: Statistical Mechanics and its Applications, 2016, vol. 444, issue C, 808-827

Abstract: We combine an axiomatics of Rényi 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. Salient issues such as concavity and Schur concavity of the new entropy are also discussed.

Keywords: Rényi’s information entropy; THC entropy; MaxEnt; Heavy-tailed distributions; Multifractals (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:444:y:2016:i:c:p:808-827

DOI: 10.1016/j.physa.2015.10.084

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