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 (cs2) 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 cs2. © 2018, The Author(s).