Towards information theory for q-nonextensive statistics without q-deformed distributions

Petr Jizba and Toshihico Arimitsu

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 76-84

Abstract: In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for systems with embedded self-similarity and q-nonextensivity. We find that this entropy can be uniquely solved in terms of a one-parameter family of information measures. The corresponding entropy maximizer is expressible via a special function known under the name of the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and make some remarks on the possible applications.

Keywords: Information theory; Rényi's information measure; Tsallis–Havrda–Charvát entropy; MaxEnt principle; Lambert W-function (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:76-84

DOI: 10.1016/j.physa.2006.01.038

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