Speed of Sound in Hadronic matter using Non-extensive Tsallis Statistics

TL;DR

This study investigates how non-extensive Tsallis statistics affect the speed of sound in hadronic matter, revealing the impact of non-equilibrium conditions on phase transition signatures in heavy-ion collisions.

Contribution

It introduces a calculation of the speed of sound using Tsallis statistics for hadron resonance gases, highlighting the influence of non-extensivity on critical behavior.

Findings

Speed of sound decreases with heavier particles, similar to equilibrium cases.

The critical behavior in speed of sound vanishes for q > 1.13.

The temperature at which mass cut-off begins varies with q.

Abstract

The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different $q$-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly present that the temperature where the mass cut-off starts, varies with the $q$-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of $q$ above approximately 1.13 all criticality disappear in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of $q$, disappears completely.