Construction of relativistic hydrodynamics of a multicomponent fluid. 1. The method of relativistic irreversible thermodynamics

The paper develops relativistic mechanics and irreversible thermodynamics of a cosmological liquid mixture in which thermal conduction, diffusion, viscous flow and their crossing phenomena can occur. The main thermodynamic fields that occur in relativistic irreversible thermodynamics are defined as statistical expressions using relativistic kinetics. The effects of the Eckart approach on the choice of the hydrodynamic velocity are shown. The equations of relativistic multicomponent hydrodynamics for local densities of momentum, energy and number of particles of different sort, are also obtained from the fundamental conservation laws of relativistic thermodynamics.. The energy conservation law (the first beginning of relativistic thermodynamics) is formulated. Covariant Gibbs relation and local form of the second principle of thermodynamics in the presence of entropy source were derived in order to obtain determining relations linearly connecting fluxes with corresponding thermodynamic forces. Equivalent forms of relativistic entropy production in the form of a bilinear expression in terms of thermodynamic forces were obtained. A new cross-effect between diffusion and conduction arising from the relativistic term in the thermodynamic force coupled to the heat flux is discussed. The synopsis presented is of interest for relativistic mechanics, astrophysics, and cosmology.