Fluctuations, correlations and the nonextensivity

TL;DR

This paper explores how correlations affect Tsallis' nonextensive statistics, showing that correlations can make entropy additive and that the nonextensivity parameter approaches unity as the system size grows, linking energy distributions to multiplicity distributions.

Contribution

It demonstrates how correlations influence nonextensive entropy and connects Tsallis distributions to Negative Binomial multiplicity distributions in physical systems.

Findings

Correlations can render Tsallis entropy additive.

The effective nonextensivity parameter approaches 1 with increasing variables.

Tsallis energy distributions lead to Negative Binomial multiplicity distributions.

Abstract

Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis entropy additive and that the effective nonextensivity parameter $q_N$ decreases towards unity when the number of variables $N$ increases. We demonstrate that Tsallis distribution of energies of particles in a system leads in natural way to the Negative Binomial multiplicity distribution in this system.