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

Author

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  • Jizba, Petr
  • Arimitsu, Toshihico

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.

Suggested Citation

  • Jizba, Petr & Arimitsu, Toshihico, 2006. "Towards information theory for q-nonextensive statistics without q-deformed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 76-84.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:76-84
    DOI: 10.1016/j.physa.2006.01.038
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    Cited by:

    1. Oikonomou, Thomas & Tirnakli, Ugur, 2009. "Generalized entropic structures and non-generality of Jaynes’ Formalism," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3027-3034.

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