Physics
Hard disks in 2D: elastic collisions conserve energy & momentum. Starting from any initial condition, the system ergodically explores phase space and the velocity distribution converges to:
f(v) = (m/2πkT) exp(−mv²/2kT)
This is the Maxwell-Boltzmann distribution — Boltzmann's H-theorem guarantees entropy increases until this equilibrium is reached.
The histogram (blue) should match the MB curve (orange dashed) at equilibrium. Watch it emerge from the initial delta-function distribution!