Kinetic Theory of Chiral Active Disks: Odd Transport and Torque Density

Abstract: Parity-odd transport is a central signature of chiral fluids, yet analytical predictions are sparse. Here, we introduce a minimal two-dimensional hard-disk gas in which chirality arises solely from a collision-induced transverse impulse. Motivated by granular spinners, collisions are dissipative and inject orbital angular momentum through a fixed tangential ``kick'' at contact. Starting from a Boltzmann-Enskog description, we derive nonlinear hydrodynamic equations for density, momentum, and temperature, and show that chirality generates an antisymmetric homogeneous stress corresponding to a nonzero torque density. In the dilute limit, a Chapman-Enskog expansion yields analytical predictions for transport coefficients, including odd viscosity, odd thermal conductivity, and odd self-diffusivity, in good agreement with numerical simulations. This minimal kinetic model can serve as a foundation for systematic coarse-graining of chiral fluids and as a tractable benchmark for gaining insight into odd transport across a broader class of chiral systems.