Derivation of second-order relativistic hydrodynamics for reactive multicomponent systems

We derive the second-order hydrodynamic equation for reactive multicomponent systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation laws during the collision process. Our derivation is based on the renormalization-group method, in which the Boltzmann equation is solved in an organized perturbation method as faithfully as possible and possible secular terms are resummed away by a suitable setting of the initial value of the distribution function. The microscopic formulas of the relaxation times and the lengths are explicitly given as well as those of the transport coefficients for the reactive multicomponent system. The resultant hydrodynamic equation with these formulas has nice properties that it satisfies the positivity of the entropy-production rate and the Onsager's reciprocal theorem, which ensure the validity of our derivation.