title: The Chiral Thermostat subtitle: H-theorem survives chiral collisions date: 2026-02-26 paper: Lier & Matus, arXiv:2602.21367

Two disks collide. In a normal gas, the collision is symmetric — swap the incoming and outgoing trajectories and you get a valid collision going backward. This is time-reversal symmetry, and it's the foundation on which the Boltzmann H-theorem rests: entropy can't decrease, and a gas of colliding particles relaxes toward equilibrium. Lier and Matus break time-reversal symmetry at the microscopic level. Their disks collide chirally — the scattering angle is rotated by a fixed offset, so the collision rule distinguishes clockwise from counterclockwise. Run the trajectory backward and you don't get a valid collision. The microscopic dynamics are fundamentally asymmetric. The surprise: the H-theorem still holds. The gas still relaxes to equilibrium. The chiral collision rule conserves energy and momentum — it just redirects them differently than a symmetric collision would. That's enough. The transport toward equilibrium doesn't require microscopic time-reversal symmetry. It requires conservation laws. But the transport coefficients change. A Chapman-Enskog expansion — the standard perturbative procedure for extracting macroscopic fluid properties from microscopic kinetics — yields analytical expressions for the shear viscosity, thermal conductivity, and a new quantity: odd viscosity. Odd viscosity is the antisymmetric part of the viscosity tensor. Normal viscosity dissipates energy; odd viscosity doesn't. It produces forces perpendicular to the velocity gradient — like the Coriolis force, but arising from collision geometry rather than rotation. The gas swirls without losing energy. Molecular dynamics simulations confirm the analytical predictions. The equilibrium state is the same as a normal gas. The transport to that equilibrium is different — shaped by chirality — but the destination is identical. The distinction between dynamics and destination matters here. Breaking time-reversal symmetry changes how the gas flows but not where it flows to. The equilibrium state is determined by what's conserved (energy, momentum, particle number), not by how collisions redistribute those quantities. The path depends on the rule. The fixed point depends on the constraints.