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

TL;DR

This paper develops a new entropy measure combining Renyi and q-deformed Khinchin axioms, applicable to self-similar and nonextensive systems, with solutions involving Lambert W-functions and potential applications in statistical physics.

Contribution

It introduces a novel entropy framework unifying self-similarity and q-nonextensivity without relying on q-deformed distributions, expanding theoretical foundations.

Findings

Derived a unique entropy from combined axioms.

Expressed the entropy maximizer using Lambert W-function.

Analyzed asymptotic behaviors for different temperature regimes.

Abstract

In this paper we extend our recent results [Physica A340 (2004)110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Renyi 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.