Thermodynamics with fractal structure, Tsallis statistics and hadrons

TL;DR

This paper introduces a thermodynamical model with fractal structure using Tsallis statistics, linking fractal dimensions to the entropic index and connecting thermodynamics with microscopic interactions via the S-matrix.

Contribution

It demonstrates that Tsallis statistics effectively describes thermodynamics of fractal systems and relates fractal dimensions to the entropic index q.

Findings

Fractal thermodynamics is compatible with Tsallis statistics.

Fractal dimensions are expressed in terms of the entropic index q.

Connections between thermodynamics and microscopic interactions are established.

Abstract

A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and its Lipshitz-H\"older exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data is discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the S-matrix.