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 ($$\eta $$ η ), bulk viscosity ($$\zeta $$ 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 $$\eta /s$$ η/s and $$\zeta /s$$ ζ/s decrease rapidly with temperature (T) for various q-values. As q increases, the magnitudes of $$\eta /s$$ η/s and $$\zeta /s$$ 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 ($$\kappa _T$$ κT ) using non-extensive Tsallis statistics at finite baryon chemical potential ($$\mu _B$$ μB ). It is observed that, $$\kappa _T$$ κT changes significantly with the degree of non-extensivity. We also study the squared speed of sound ($$c_{s}^{2}$$ 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 $$c_{s}^{2}$$ cs2