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 (𝜂), bulk viscosity (𝜁) 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 𝜂/𝑠 and 𝜁/𝑠 decrease rapidly with temperature (T) for various q-values. As q increases, the magnitudes of 𝜂/𝑠 and 𝜁/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 (𝜅𝑇) using non-extensive Tsallis statistics at finite baryon chemical potential (𝜇𝐵). It is observed that, 𝜅𝑇 changes significantly with the degree of non-extensivity. We also study the squared speed of sound (𝑐2𝑠) 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 𝑐2𝑠.