Stochastic dynamics of N correlated binary variables and non-extensive statistical mechanics

TL;DR

This paper introduces a dynamical model of correlated binary variables on a ring, illustrating how non-extensive statistical mechanics and q-Gaussian distributions can emerge from microscopic dynamics.

Contribution

It presents a new dynamical model linking microscopic binary variable flips to non-extensive statistical mechanics and Tsallis entropy.

Findings

Model exhibits extensivity of Tsallis entropy with q<1

System shows emergence of q-Gaussian distribution

Provides insight into mesoscopic dynamics from microscopic rules

Abstract

The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the thermodynamic limit the extensivity of the Tsallis entropy with q<1 as well as a q-Gaussian distribution. The dynamical model consists of a one-dimensional ring of particles characterized by correlated binary random variables, which are allowed to flip according to a simple random walk rule. The proposed dynamical model provides an insight how a mesoscopic dynamics characterized by the non-extensive statistical mechanics could emerge from a microscopic description of the system.