Maximum entropy approach to central limit distributions of correlated variables

TL;DR

This paper derives the analytical entropy form for correlated variables' limit distributions using the maximum entropy principle, showing these are not q-Gaussians and cannot be obtained via Tsallis entropy.

Contribution

It introduces a new entropy formulation that accurately describes the limit distributions of correlated variables, expanding beyond q-Gaussian models.

Findings

Derived the analytical entropy form for correlated variables' distributions.

Showed these distributions are not q-Gaussians.

Established that Tsallis entropy cannot reproduce these distributions.

Abstract

Hilhorst and Schehr recently presented a straight forward computation of limit distributions of sufficiently correlated random numbers \cite{hilhorst}. Here we present the analytical form of entropy which --under the maximum entropy principle (with ordinary constraints)-- provides these limit distributions. These distributions are not $q$-Gaussians and can not be obtained with Tsallis entropy.