Correlated Gaussian systems exhibiting additive power-law entropies

TL;DR

This paper demonstrates that a specific power-law entropy can be extensive for correlated Gaussian systems without relying on physical models, by characterizing the necessary correlations among components.

Contribution

It shows that $S_q$ entropy with $0<q<1$ can be extensive in Gaussian systems through particular correlations, providing a purely statistical foundation.

Findings

Power-law $q$-entropy can be extensive in Gaussian systems.

Extensivity depends on specific correlations among variables.

Characterization of the correlations that lead to extensivity.

Abstract

We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in \mathbb{R}^N$ are distributed according to a Gaussian probability distribution $f$, the associated entropy $S_q(X)$ exhibits the extensivity property for special types of correlations among the $X_i$. We also characterize this kind of correlation.