Classical microscopic derivation of the relativistic hydrodynamics equations

Abstract: We present microscopic derivation of the relativistic hydrodynamics (RHD) equations directly from mechanics omitting derivation of kinetic equation. We derive continuity equation and energy-momentum conservation law. We also derive equation of evolution of particles current. In non-relativistic hydrodynamics equation of particles current evolution coincide with the equation of momentum evolution, the Maxwell's equations contain concentration and electric current (which proportional to the particles current), so, to get a close set of equations we should have equations of evolution of the concentration and the particles current. Evolution of the particles current depends on the electrical and magnetic fields. Thus, we obtain the set of the RHD equations as the set of the continuity equation, the equation of particles current and the Maxwell equations. This approximation does not require to include the evolution of momentum and allows to consider physical problems. Certainly, particles current evolution equation contains some new functions which we can express via concentration and particles current or we can derive equation for this functions, and, thus, get to more general approximation. This approximation also developed and discussed in this paper.