Influence of global correlations on central limit theorems and entropic extensivity

John A. Marsh, Miguel A. Fuentes, Luis G. Moyano and Constantino Tsallis

Physica A: Statistical Mechanics and its Applications, 2006, vol. 372, issue 2, 183-202

Abstract: We consider probabilistic models of N identical distinguishable, binary random variables. If these variables are strictly or asymptotically independent, then, for N→∞, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the Boltzmann-Gibbs-Shannon entropy SBGS≡-∑i=1Wpilnpi (where W=2N) is extensive, meaning that SBGS(N)∼N. If these variables have any nonvanishing global (i.e., not asymptotically independent) correlations, then the attractor deviates from the Gaussian. The entropy appears to be more robust, in the sense that, in some cases, SBGS remains extensive even in the presence of strong global correlations. In other cases, however, even weak global correlations make the entropy deviate from the normal behavior. More precisely, in such cases the entropic form Sq≡1q-1(1-∑i=1Wpiq) (with S1SBGS) can become extensive for some value of q≠1. This scenario is illustrated with several new as well as previously described models. The discussion illuminates recent progress into q-describable nonextensive probabilistic systems, and the conjectured q-Central Limit Theorem (q-CLT) which posses a q-Gaussian attractor.

Keywords: Nonextensive statistical mechanics; Entropic extensivity; Central limit theorems; Global correlations (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:372:y:2006:i:2:p:183-202

DOI: 10.1016/j.physa.2006.08.009

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