Random matrices ensembles and the extensivity of the Sq entropy

TL;DR

This paper investigates how the nonadditive entropy S_q behaves in certain correlated random matrix models, showing it is extensive only at q=1 unless phase space restrictions are applied.

Contribution

It demonstrates the conditions under which the nonadditive entropy S_q becomes extensive in correlated random matrix ensembles, highlighting the role of phase space restrictions.

Findings

S_q is extensive only as q approaches 1 in the studied models

Phase space restrictions can make S_q extensive for q ≠ 1

Correlated random matrices exhibit scale-invariant properties

Abstract

We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy $S_q$ is extensive only when the limit $q\rightarrow 1$ is taken. On the other hand, when restriction in the occupation of the phase space is imposed extensiveness is obtained for values of the entropic parameter different of one.