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 AND THEORETICAL PHYSICS

Elsevier

Año: 2006 p. 183 - 202

0378-4371

We consider probabilistic models of N identical distinguishable,binary random variables. If these variables are strictly orasymptotically independent, then, for N going to infinity, (i)the attractor in distribution space is, according to the standardcentral limit theorem, a Gaussian, and (ii) theBoltzmann-Gibbs-Shannon entropy, Sb, is extensive. If thesevariables have any nonvanishing global (i. e. non asymptoticallyindependent) correlation, then the attractor deviates from theGaussian. The entropy appears to be more robust, in the sensethat, in some cases, Sb remains extensive even in the presence ofstrong global correlations. In oder cases, however, even weakglobal correlations make the entropy deviate from the normalbehavior. More precisely, in such cases the entropic form Sq, canbecome extensive for some value of q different from one. Thisscenario is illustrated with several new as well as previouslydescribed models. The discution illuminates recent progress intoq-describable nonextensive probabilistic system.