On the extensivity of the entropy Sq, the q-generalized central limit theorem and the q-triplet
Constantino Tsallis

TL;DR
This paper reviews the conditions for the extensivity of the entropy Sq, explores a q-generalized central limit theorem, and discusses the q-triplet in solar wind data in relation to space dimension and interaction range.
Contribution
It provides a comprehensive review of the conditions for entropy Sq extensivity, discusses a possible q-generalized central limit theorem, and analyzes the q-triplet in solar wind data in relation to space and interaction parameters.
Findings
Conditions for entropy Sq extensivity summarized.
Discussion of a q-generalized central limit theorem.
Analysis of the q-triplet in solar wind and its relation to space parameters.
Abstract
First, we briefly review the conditions under which the entropy can be extensive (Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA (2005), in press; cond-mat/0502274), as well as the possible -generalization of the central limit theorem (Moyano, Tsallis and Gell-Mann, cond-mat/0509229). Then, we address the -triplet recently determined in the solar wind (Burlaga and Vinas, Physica A {\bf 356}, 375 (2005)) and its possible relation with the space-dimension and with the range of the interactions (characterized by , the attractive potential energy being assumed to decay as at long distances ).
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