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

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 $S_q$ can be extensive (Tsallis, Gell-Mann and Sato, Proc. Natl. Acad. Sc. USA (2005), in press; cond-mat/0502274), as well as the possible $q$-generalization of the central limit theorem (Moyano, Tsallis and Gell-Mann, cond-mat/0509229). Then, we address the $q$-triplet recently determined in the solar wind (Burlaga and Vinas, Physica A {\bf 356}, 375 (2005)) and its possible relation with the space-dimension $d$ and with the range of the interactions (characterized by $\alpha$, the attractive potential energy being assumed to decay as $r^{-\alpha}$ at long distances $r$).