Relaxation Time Approximation for a multi-species relativistic gas

TL;DR

This paper extends the relaxation time approximation for the relativistic Boltzmann equation to multi-species systems, incorporating momentum-dependent relaxation times and ensuring conservation laws and thermodynamic consistency.

Contribution

It introduces a generalized collision term with counter-terms for multiple particle species, enabling more accurate modeling of relativistic gases.

Findings

Derived first-order Chapman-Enskog corrections for hadron-resonance gas.

Ensured the collision term obeys the second law of thermodynamics.

Demonstrated the approach's compatibility with local conservation laws.

Abstract

We generalize a recent prescription for the relaxation time approximation for the relativistic Boltzmann equation for systems with multiple particle species at finite temperature. This is performed by adding counter-terms to the traditional Anderson-Witting ansatz for each particle species. Our approach allows for the use of momentum-dependent relaxation times and the obedience of local conservation laws regardless of the definition of the local equilibrium state. As an application, we derive the first order Chapman-Enskog corrections to the equilibrium distribution and display results for the hadron-resonance gas. We also demonstrate that our collision term ansatz obeys the second law of thermodynamics.