Chemical freezeout parameters within generic nonextensive statistics

TL;DR

This paper introduces a generalized nonextensive statistical approach to describe particle production in heavy-ion collisions, showing it better fits experimental data than traditional models and aligns with known thermodynamic phase diagrams.

Contribution

The work develops a generic nonextensive statistics framework within the hadron resonance gas model, encompassing Boltzmann-Gibbs and Tsallis statistics as special cases, to analyze particle ratios across a wide energy range.

Findings

Nonextensive statistics better reproduces particle ratios than BG or Tsallis.

Freezeout parameters are consistent with the traditional phase diagram.

The nonextensivity is characterized by two critical exponents (c, d).

Abstract

The particle production in relativistic heavy-ion collisions seems to be created in a dynamically disordered system which can be best described by an extended exponential entropy. In distinguishing between the applicability of this and Boltzmann-Gibbs (BG) in generating various particle-ratios, generic (non)extensive statistics (GNS) is introduced to the hadron resonance gas model. Accordingly, the degree of (non)extensivity is determined by the possible modifications in the phase space. Both BG extensivity and Tsallis nonextensivity are included as very special cases defined by specific values of the equivalence classes $(c, d)$. We found that the particle ratios at energies ranging between $3.8$ and $2760~$GeV are best reproduced by nonextensive statistics, where $c$ and $d$ range between $\sim0.9$ and $\sim1$. The present work aims at illustrating that the proposed approach is well capable to manifest the statistical nature of the system on interest. We don't aim at highlighting deeper physical insights. In other words, while the resulting nonextensivity is neither BG nor Tsallis, the freezeout parameters are found very compatible with BG and accordingly with the well-known freezeout phase-diagram, which is in an excellent agreement with recent lattice calculations. We conclude that the particle production is nonextensive but should not necessarily be accompanied by a radical change in the intensive or extensive thermodynamic quantities, such as internal energy and temperature. Only, the two critical exponents defining the equivalence classes $(c, d)$ are the physical parameters characterizing the (non)extensivity.