Fractal structure of hadrons and non-extensive statistics

TL;DR

This paper explores the fractal nature of hadronic systems and their connection to non-extensive thermodynamics, discussing scale invariance and proposing a diagrammatic calculation method.

Contribution

It introduces a framework linking fractal structures in hadrons to non-extensive statistics and develops a diagrammatic approach for thermodynamic calculations.

Findings

Fractal thermodynamics exhibit scale invariance.

A diagrammatic method for calculations is proposed.

Fractal structures influence non-extensive statistical behavior.

Abstract

The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years, in particular the existence of a fractal structure in thermodynamic functions for hadronic systems. We investigate the properties of such fractal thermodynamical systems, in particular the fractal scale invariance is discussed in terms of the Callan-Symanzik~equation. Finally, we propose a diagrammatic method for calculations of relevant quantities.