Radial Flow in Non-Extensive Thermodynamics and Study of Particle Spectra at LHC in the Limit of Small $(q-1)$

TL;DR

This paper develops a Taylor expansion approach for the Tsallis distribution near q=1 to analyze deviations in particle spectra from thermal equilibrium in high-energy collisions, incorporating collective flow effects.

Contribution

It introduces an analytical first-order expansion of the Tsallis distribution in (q-1) and compares it with experimental LHC data, enhancing understanding of non-extensive thermodynamics.

Findings

Analytical formulas for Tsallis distribution with flow up to first order in (q-1)

Good agreement with LHC particle spectra data

Thermodynamic consistency of the expanded distribution

Abstract

We expand the Tsallis distribution in a Taylor series of powers of (q-1), where q is the Tsallis parameter, assuming q is very close to 1. This helps in studying the degree of deviation of transverse momentum spectra and other thermodynamic quantities from a thermalized Boltzmann distribution. After checking thermodynamic consistency, we provide analytical results for the Tsallis distribution in the presence of collective flow up to the first order of (q-1). The formulae are compared with the experimental data.