Chapman-Enskog expansion for chirally colliding disks

Abstract

We study a two-dimensional gas of hard disks undergoing chiral, energy- and momentum-conserving collisions. We propose a simple chiral collision rule and show that it can effectively capture collisions of spinning noncircular particles without retaining spin or orientation as kinetic variables. Despite the microscopic breaking of time-reversal symmetry, the H-theorem is obeyed, guaranteeing relaxation towards equilibrium in the absence of external forces. A Chapman-Enskog expansion yields analytical expressions for the shear and odd viscosity and the thermal conductivity. Theoretical predictions are confirmed by nonequilibrium molecular dynamics simulations