The imprints of superstatistics in multiparticle production processes

TL;DR

This paper reviews how Tsallis nonextensive statistics manifest in multiparticle production, highlighting power law distributions, fluctuation sum rules, and the implications for nuclear collision data analysis.

Contribution

It introduces sum rules linking different fluctuation parameters and generalizes thermodynamic uncertainty relations within the superstatistics framework.

Findings

Power law distributions characterized by q > 1 are ubiquitous.

Fluctuation sum rules enable combined analysis of different observables.

Standard Tsallis distribution with q < 1 corresponds to q' = 2 - q > 1.

Abstract

We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter q > 1. In nuclear collisions one additionally observes a q-dependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters q obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard's thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity q < 1, the corresponding standard Tsallis distribution is described by q' = 2 - q > 1.