Dissipative Properties and Isothermal Compressibility of Hot and Dense Hadron Gas using Non-extensive Statistics

Abstract

We evaluate the transport properties such as shear viscosity ($\eta$), bulk viscosity ($\zeta$) and their ratios over entropy density ($s$) for hadronic matter using relativistic non-extensive Boltzmann transport equation (NBTE) in relaxation time approximation (RTA). In NBTE, we argue that the system far from equilibrium may not reach to an equilibrium described by extensive (Boltzmann-Gibbs (BG)) statistics but to a $q$-equilibrium defined by Tsallis non-extensive statistics after subsequent evolution, where $q$ denotes the degree of non-extensivity. We observe that $\eta /s$ and $\zeta /s$ decrease rapidly with temperature ($T$) for various $q$-values. As $q$ increases, the magnitudes of $\eta /s$ and $\zeta /s$ decrease with $T$. We also show the upper mass cutoff dependence of these ratios for a particular $q$ and find that they decrease with the increase in mass cutoff of hadrons. Further, we present the first estimation of isothermal compressibility (${\kappa }_T$) using non-extensive Tsallis statistics at finite baryon chemical potential (${\mu }_B$). It is observed that, ${\kappa }_T$ changes significantly with the degree of non-extensivity. We also study the squared speed of sound ($c_s^2$) as a function of temperature at finite baryon chemical potential for various $q$ and upper mass cutoffs. It is noticed that there is a strong impact of $q$ and mass cutoff on the behaviour of $c_s^2$.

Comments: Same as published version