Where it shows up
This relaxation onto Maxwell-Boltzmann reaches well beyond a tray of billiard balls. It is why any gas left alone settles to a single temperature, why the nitrogen and oxygen molecules in the air around you share this exact speed profile, and why the stars in a globular cluster (trading energy gravitationally rather than mechanically) drift towards a similar equilibrium. Semiconductor engineers borrow the electron version to model thermal noise in a resistor, and atmospheric chemists watch the high-speed tail to predict reaction rates, since only the rare fast molecules carry enough energy to clear an activation barrier. The general lesson is that many random elastic exchanges erase how you started and leave one distribution behind, set only by the average energy.
The knobs
- Particle count: how many discs share the box. More discs mean more collisions each second, so the histogram fills in faster and reads smoother. Changing it reseeds the gas.
- Temperature: the initial speed scale, which fixes the average energy. Nudge it and every velocity is rescaled live, sliding the whole distribution towards faster or slower speeds.
- Disc radius: the size of each disc, and therefore its collision cross-section. Fatter discs bump into each other more often and thermalise sooner. Changing it reseeds the gas.
- Speed: a pure control on the simulation clock. It rescales how quickly the dance plays out without touching the physics or the equilibrium shape.