# Quasi-Power Law Ensembles: Nonextensive Statistics or Superstatistics

## TL;DR

This paper explores how power-law distributions in particle physics can arise from temperature fluctuations, offering a way to distinguish different fluctuation mechanisms in high-energy collisions.

## Contribution

The paper introduces a method to differentiate between event-by-event and event-to-event temperature fluctuations in particle production.

## Key findings

- Temperature fluctuations can generate Tsallis-like power-law distributions without nonextensive statistics.
- Such fluctuations induce inter-particle correlations in emitted hadrons.
- The proposed strategy helps characterize high-multiplicity states at the Large Hadron Collider.

## Abstract

In phenomenological studies of multiparticle production, transverse-momentum spectra measured in experiments frequently display an approximately power-law falloff, for which the Tsallis-type functional form is commonly employed as an effective parametrization. Within this framework, the emergence of such spectra is interpreted as a manifestation of nonextensive statistical behavior. An analogous power-law structure, however, can be reproduced without explicitly postulating Tsallis statistics by assuming the presence of intrinsic fluctuations of the local temperature (T) in the hadronizing medium; in that case, the observed deviations from a purely exponential spectrum are encapsulated by the nonextensivity index (q). We show that temperature fluctuation mechanisms capable of generating Tsallis-like power-law distributions in multiparticle production necessarily induce nontrivial inter-particle correlations among the emitted hadrons. Building on this observation, we outline a strategy to discriminate fluctuations realized on an event-by-event basis from those arising predominantly through event-to-event variability. Such a separation may be particularly pertinent for the characterization of high-multiplicity (high-density) final states produced at the Large Hadron Collider.