Towards information theory for q-nonextensive statistics without q-deformed distributions
arXiv:cond-mat/0510092 · doi:10.1016/j.physa.2006.01.038
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.
Presented at Next2005, uses Elsevier LaTeX macros, revised version with minor changes, accepted to Physica A