Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

Abstract

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of ${N}_{\mathrm{spec}}$ particle species with ${N}_{q}$ intrinsic quantum numbers (e.g., electric charge, baryon number, and strangeness) using the method of moments. We obtain the continuity equations for multiple conserved charges as well as the conservation equations for the total energy and momentum in the single-fluid approximation. These $4+{N}_{q}$ conservation laws are closed by deriving the second-order equations of motion for the dissipative quantities in the $(10+4{N}_{q})$-moment approximation. The resulting fluid-dynamical equations are formally similar to those of a single-component system, but feature different thermodynamic relations and transport coefficients. We derive general relations for all transport coefficients and compute them explicitly in the ultrarelativistic limit.