On the derivation, in the framework of the Tsallis statistics, of relativistic hydrodynamic equations for a rarefied non-ideal gas system of high-energy particles

Abstract

In the paper the construction of non-extensive relativistic dissipative hydrodynamics of identical particles on the basis of the relativistic kinetic equation obtained in a q-non-extensive context of Tsallis statistics and taking into account inclusion of correlation effects (by rejecting the molecular chaos hypothesis ) into the collision term. It is shown that the local collision equilibrium is described by a generalized version of the Yuttner relativistic distribution. With the help of this distribution all thermodynamic parameters of state are defined in explicit form. Linear constitutive relations and transport coefficients such as shear viscosity, bulk viscosity and heat conductivity are derived from the linearized collision integral written in the Anderson-Witting form and evaluated using a relaxation time approximation. The designed non-extensive relativistic fluid dynamics is designed to simulate a wide range of phenomena in astrophysics, cosmology and high-energy physics