Granular Gas — Inelastic Maxwell Model & Haff's Law Cooling
The inelastic Maxwell model: kinetic energy is lost in each collision (restitution e<1), causing the granular gas to cool. Haff's law predicts T(t) ∝ 1/(1+t/t*)² — algebraic cooling, not exponential. Crucially, the velocity distribution P(v) develops a non-Gaussian high-velocity tail ∝ exp(−c|v|), a hallmark of inelasticity distinct from thermal equilibrium.