Tsallis statistics, fractals and QCD

TL;DR

This paper explores the application of Tsallis non-extensive statistics to quantum chromodynamics (QCD) and high-energy physics, linking fractal structures of hadrons with scaling properties of gauge fields, and deriving the Tsallis index from field theory parameters.

Contribution

It introduces a novel connection between Tsallis statistics and fractal structures in hadrons, deriving the entropic index from gauge theory parameters and matching experimental data.

Findings

Tsallis index $q$ matches experimental values.

Gauge fields exhibit fractal, self-similar structures.

Scaling properties relate to fractal behavior in QCD.

Abstract

We study the non-extensive Tsallis statistics and its applications to QCD and high energy physics, and analyze the possible connections of this statistics with a fractal structure of hadrons. Then, we describe how scaling properties of Yang-Mills theories allow the appearance of self-similar structures in gauge fields, which actually behave as fractals. The Tsallis entropic index, $q$, is deduced in terms of the field theory parameters, resulting in a good agreement with the value obtained experimentally.