Derivation of second-order relativistic hydrodynamics for reactive multi-component systems

TL;DR

This paper derives a second-order relativistic hydrodynamic equation for reactive multi-component systems from the Boltzmann equation using the renormalization group method, providing explicit formulas for transport coefficients and ensuring thermodynamic consistency.

Contribution

It introduces a novel derivation of second-order hydrodynamics for reactive multi-component systems using the RG method, including explicit microscopic formulas for relaxation times and transport coefficients.

Findings

Hydrodynamic equations satisfy entropy production positivity.

The equations obey Onsager's reciprocal relations.

Explicit formulas for relaxation times and transport coefficients are provided.

Abstract

We derive the second-order hydrodynamic equation for reactive multi-component 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 (RG) 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 formulae of the relaxation times and the lengths are explicitly given as well as those of the transport coefficients for the reactive multi-component system. The resultant hydrodynamic equation with these formulae 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.