Shear viscosity of an ultrarelativistic Boltzmann gas with isotropic inelastic scattering processes

TL;DR

This paper derives an analytic formula for the shear viscosity of an ultrarelativistic gas considering both elastic and inelastic scattering processes, validated by kinetic transport calculations.

Contribution

It provides a new analytic expression for shear viscosity including inelastic processes, based on the entropy principle and Grad's approximation.

Findings

Analytic shear viscosity formula matches kinetic transport results.

Shear viscosity depends on elastic and inelastic cross sections.

Validation confirms the formula's accuracy for ultrarelativistic gases.

Abstract

We derive an analytic expression for the shear viscosity of an ultra-relativistic gas in presence of both elastic $2\to 2$ and inelastic $2\leftrightarrow 3$ processes with isotropic differential cross sections. The derivation is based on the entropy principle and Grad's approximation for the off-equilibrium distribution function. The obtained formula relates the shear viscosity coefficient $\eta$ to the total cross sections $\sigma_{22}$ and $\sigma_{23}$ of the elastic resp. inelastic processes. The values of shear viscosity extracted using the Green-Kubo formula from kinetic transport calculations are shown to be in excellent agreement with the analytic results which demonstrates the validity of the derived formula.