Lattice QCD thermodynamics and RHIC-BES particle production within generic nonextensive statistics

TL;DR

This paper reviews the application of Tsallis nonextensive statistics in high-energy physics, critiques its current implementation, and proposes a more comprehensive approach to better match lattice QCD results and particle production data.

Contribution

It introduces a novel interpretation of the Tsallis-temperature and suggests modifications to the statistical framework to incorporate correlations and nonextensivity more accurately.

Findings

Lattice QCD thermodynamics is consistent with extensive Boltzmann-Gibbs statistics.

The low Tsallis-temperature may result from incomplete algebraic implementation.

Particle ratios at RHIC-BES energies are likely nonextensive, but not necessarily Tsallis-type.

Abstract

The current status of implementing Tsallis (nonextensive) statistics on high-energy physics is briefly reviewed. The remarkably low freezeout-temperature, which apparently fails to reproduce the first-principle lattice QCD thermodynamics and the measured particle ratios, etc. is discussed. The present work suggests a novel interpretation for the so-called {\it "Tsallis-temperature"}. It is proposed that the low Tsallis-temperature is due to incomplete implementation of Tsallis algebra though exponential and logarithmic functions to the high-energy particle-production. Substituting Tsallis algebra into grand-canonical partition-function of the hadron resonance gas model seems not assuring full incorporation of nonextensivity or correlations in that model. The statistics describing the phase-space volume, the number of states and the possible changes in the elementary cells should be rather modified due to interacting correlated subsystems, of which the phase-space is consisting. Alternatively, two asymptotic properties, each is associated with a scaling function, are utilized to classify a generalized entropy for such a system with large ensemble (produced particles) and strong correlations. Both scaling exponents define equivalence classes for all interacting and noninteracting systems and unambiguously characterize any statistical system in its thermodynamic limit. We conclude that the nature of lattice QCD simulations is apparently extensive and accordingly the Boltzmann-Gibbs statistics is fully fulfilled. Furthermore, we found that the ratios of various particle yields at extreme high and extreme low energies of RHIC-BES is likely nonextensive but not necessarily of Tsallis type.