Constructing relativistic hydrodynamics of a simple fluid in a class of second-order theories. 2. The method of relativistic extended irreversible thermodynamics

In this paper we constructed thermo-hydrodynamics for relativistic fluid (taking into account the second order of deviation from equilibrium for dissipative heat and viscosity flows) on the basis of extended irreversible thermodynamics (RNT). RNT formalism, providing adequate modeling of systems close to the equilibrium state, goes beyond the local equilibrium hypothesis by expanding the number of basic independent variables (including dissipative flows), as well as by modifying such conceptual concepts as entropy, temperature and pressure. The evolutionary laws for the main nonequilibrium field quantities of the relativistic system are postulated: 4-vector particle flux, 4-vector energy-momentum and 4-vector entropy flux. In order to derive the constitutive equations, a nonlocal Gibbs covariance relation and a nonlocal form of the second principle of thermodynamics with a source of entropy due to additional variables-dissipative flows-were obtained. The defining equations of the hyperbolic type, forbidding superluminal velocities, modified by relaxation terms, have been obtained. The construction of relativistic thermodynamics is carried out using the hydrodynamic 4-speed defined by Eckart. The constructed relativistic hydrodynamics has its applications in such important fields of science as nuclear physics, astrophysics and cosmology.