Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

TL;DR

This paper derives a comprehensive multicomponent relativistic dissipative fluid dynamics framework from the Boltzmann equation, incorporating multiple conserved charges and quantum numbers, with explicit transport coefficients in the ultrarelativistic limit.

Contribution

It extends relativistic fluid dynamics to multicomponent systems with quantum numbers, providing new equations and explicit transport coefficients derived from the Boltzmann equation.

Findings

Derived multicomponent relativistic dissipative fluid equations.

Obtained explicit transport coefficients in the ultrarelativistic limit.

Unified formalism similar to single-component systems but with distinct thermodynamics.

Abstract

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ 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 $(10+4N_q)$-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.