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Equipartition Theorem: Hard-Disk Gas (2D)

2D companion to the equipartition theorem simulator: instead of a Langevin heat bath driving independent translation/rotation/vibration channels, this runs a genuine hard-disk molecular-dynamics gas — three species of different real mass, started at three different temperatures, thermalizing purely through deterministic elastic collisions until every species' measured energy per degree of freedom converges to the same value.

Physics & Mechanics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

This is the 2D companion to the 3D Langevin-bath equipartition simulator. Instead of coupling each degree of freedom to an external stochastic heat bath, this simulator runs a genuine hard-disk molecular-dynamics gas: three species of disk with different real mass — light, medium and heavy — share one box, each species started at a deliberately different mean kinetic energy per particle. From that point on the simulation is fully deterministic: disks fly in straight lines, bounce elastically off the walls, and exchange momentum and energy only through pairwise elastic collisions that conserve both quantities exactly. There is no randomness, no thermostat and no external energy source after the initial condition is drawn. Watch the three species' measured energy per degree of freedom — tracked live in the side panel — start apart and converge onto the same value even though their masses (and therefore their typical speeds) remain completely different, which is equipartition emerging from ergodic collision dynamics rather than being built in by a bath.

⚙ Under the hood

Three species of hard disk — light, medium and heavy — start at three different temperatures in the same box and thermalize purely through deterministic elastic collisions, no heat bath or randomness involved. Watch each species' measured energy per degree of freedom converge to the same conserved system average, demonstrating equipartition through genuine collisional molecular dynamics rather than a Langevin bath.

statistical mechanicsequipartition theoremhard-disk gasmolecular dynamicselastic collisionskinetic theory2D physics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install