Non-extensive statistics, relativistic kinetic theory and fluid dynamics

TL;DR

This paper develops a relativistic fluid dynamic framework derived from a non-extensive Boltzmann equation aligned with Tsallis' entropy, explaining particle spectra with power-law tails across various energies and systems.

Contribution

It introduces a relativistic fluid dynamics model based on non-extensive statistics, connecting Tsallis entropy with kinetic theory and deriving transport coefficients.

Findings

Power-law energy distributions fit experimental spectra.

Derived relativistic fluid equations from non-extensive Boltzmann equation.

Calculated transport coefficients like shear viscosity and heat conductivity.

Abstract

Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies, colliding system sizes, and produced hadron sorts. In order to derive its evolution one needs a corresponding dynamical description of the system which results in such final state observables. The equations of relativistic fluid dynamics are obtained from a non-extensive Boltzmann equation consistent with Tsallis' non-extensive $q$-entropy formula. The transport coefficients like shear viscosity, bulk viscosity, and heat conductivity are evaluate based on a linearized collision integral.