Renormalization group equation for Tsallis statistics

TL;DR

This paper explores the application of the renormalization group equation to Tsallis non-extensive statistics, particularly in systems with fractal structures like thermofractals, to understand their scaling properties and origins in hadronic physics.

Contribution

It introduces the formulation of a Callan-Symanzik equation for thermofractals within Tsallis statistics, linking fractal structures to non-extensive thermodynamics.

Findings

Thermofractals exhibit scaling properties described by the RG equation.

The approach connects non-extensive statistics to fractal energy-momentum structures.

Potential insights into QCD and hadronic physics origins of non-extensivity.

Abstract

The non extensive statistics proposed by C. Tsallis has found wide applicability, being present even in the description of experimental data from high energy collisions. A system with a fractal structure in its energy-momentum space, named thermofractal, was shown to be described thermodynamically by the non extensive statistics. Due to the many common features between thermofractals and Hagedorn's fireballs, this system offers the possibility to investigate the origins of non extensivity in hadronic physics and in QCD. In this regard, the investigation of the scaling properties of thermofractals through the renormalization group equation, known as Callan-Symanzik equation, can be an interesting approach.