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Equipartition Theorem — Energy per Degree of Freedom

Watch a bath of diatomic molecules translate, rotate and vibrate under Langevin thermal noise, and see their measured energy per quadratic degree of freedom converge to the equipartition prediction (1/2)k_BT, independent of mass, moment of inertia or bond stiffness.

Physics & Mechanics3DAdvanced60 FPS📱 Mobile-adapted⇄ 2D version

A box of diatomic "molecules" is coupled to a heat bath through independent Langevin equations for their three kinds of motion — translation of the whole molecule, end-over-end rotation, and bond-length vibration. Each channel is driven by the exact same fluctuation-dissipation physics that governs real thermal noise, and this simulator tracks the running average energy stored in each channel per quadratic degree of freedom. Despite translation, rotation and vibration having completely different effective masses, moments of inertia and stiffness, all three measured averages converge to the same value: (1/2)k_BT per degree of freedom, exactly as the equipartition theorem predicts. Sliders let you change temperature, the bath coupling strength, and the bond's spring constant to see which quantities shift the equilibrium value (only T) and which only change how fast or how noisily it's reached.

⚙ Under the hood

A bath of diatomic molecules translates, rotates and vibrates under independent Langevin thermal noise, and the measured energy per quadratic degree of freedom converges live to the equipartition prediction (1/2)k_BT, regardless of mass, moment of inertia, or bond stiffness.

statistical mechanicsequipartition theoremthermodynamicsLangevin dynamicskinetic theoryheat capacity

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install