# Bag-type Model with Fractal Structure

## TL;DR

This paper introduces a fractal-structured bag model using non-extensive statistics to describe hadronic systems, deriving thermodynamic properties and analyzing the proton's internal structure and surface pressure.

## Contribution

It presents a novel bag-type model incorporating fractal geometry and non-extensive statistics to analyze hadronic properties and internal structure.

## Key findings

- Calculated the proton surface pressure as (0.135 GeV)^4.
- Derived thermodynamic quantities along the freeze-out line at 1 GeV per particle.
- Analyzed fractal structures within the proton volume.

## Abstract

In this work we present a bag-type model within a non-extensive statistics applied to the description of the properties of a hadronic system with an underlying fractal structure. The non-extensive ideal gas inside the bag is determined by the grand canonical partition function from which pressure, energy and particle density as well as temperature and chemical potential are obtained for the hadronic system. These quantities are studied in the approximation of fixed mass for all bag constituents but also for discrete and continuum masses. In all cases, the freeze-out line, corresponding to the energy per particle equal to 1 GeV and the lines corresponding to a fractal structure inside the proton volume are obtained. Finally, the pressure on the bag surface of the proton is calculated and the resulting value $(0.135\, {\rm GeV})^4$ obtained.