Perspective on Tsallis Statistics for Nuclear and Particle Physics

TL;DR

This paper reviews Tsallis statistics in high energy nuclear physics, highlighting its effective use in modeling particle distributions in collisions, with one form consistent with equilibrium principles and characterized by a nonextensitivity parameter.

Contribution

It clarifies which form of Tsallis statistics aligns with equilibrium mechanics and demonstrates its practical application in high energy collision data modeling.

Findings

Tsallis distribution effectively models particle spectra in high energy collisions.

Only one Tsallis form is consistent with equilibrium statistical mechanics.

The nonextensitivity parameter $q$ captures deviations from exponential behavior.

Abstract

This is a concise introduction to the topic of nonextensive Tsallis statistics meant especially for those interested in its relation to high energy proton-proton, proton-nucleus, and nucleus-nucleus collisions. The three types of Tsallis statistics are reviewed. Only one of them is consistent with the fundamental hypothesis of equilibrium statistical mechanics. The single particle distributions associated with it, namely Boltzmann, Fermi-Dirac, and Bose-Einstein, are derived. These are not equilibrium solutions to the conventional Boltzmann transport equation which must be modified in a rather nonintuitive manner for them to be so. Nevertheless the Boltzmann limit of the Tsallis distribution is extremely efficient in representing a wide variety of single particle distributions in high energy proton-proton, proton-nucleus, and nucleus-nucleus collisions with only three parameters, one of them being the so-called nonextensitivity parameter $q$. This distribution interpolates between an exponential at low transverse energy, reflecting thermal equilibrium, to a power law at high transverse energy, reflecting the asymptotic freedom of QCD. It should not be viewed as a fundamental new parameter representing nonextensive behavior in these collisions.