Probabilistic model of N correlated binary random variables and non-extensive statistical mechanics

TL;DR

This paper introduces a simple one-dimensional binary particle chain model that demonstrates key properties of non-extensive statistical mechanics, including entropy extensivity and q-Gaussian distributions, providing deeper physical insights.

Contribution

It presents a minimal model illustrating how non-extensive statistical mechanics properties emerge in a correlated binary system.

Findings

Entropy remains extensive for q<1 in the model.

The model exhibits q-Gaussian distributions in the large particle limit.

Provides a physical interpretation of non-extensive properties.

Abstract

The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some important properties described by the non-extensive statistical mechanics are useful to provide deeper physical insights. In this article we present a simple model, consisting of a one-dimensional chain of particles characterized by binary random variables, that exhibits both the extensivity of the generalized entropy with q<1 and a q-Gaussian distribution in the limit of the large number of particles.