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

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We derive an analytic expression for the shear viscosity of an ultra-relativistic gas in presence of both elastic 2→ 2 and inelastic 2↔ 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 η to the total cross sections σ₂₂ and σ₂₃ 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.