Silicon Logic
SL · 05 · Entropy
§ 05 · Sandbox · Statistical mechanics Filed 2026.05

Five hundred particles, and one direction in time.

A box of dust on a dark table. Press play and watch it spread. Then try, with a soft brush of your finger, to push every grain back into the corner you started from. You will fail — not because the brush is too weak, but because the universe has more ways of being shuffled than of being neat, and arithmetic, not friction, is what stops you.

Mode   Gas · one species N   500 Cells   192
State   ▶ live Microstates   10⁰ S/Smax   0.00
Press play · drag inside to push particles like a brush
Experiment
Brush strength
100
Show
Sandbox

Reading the picture

§ 05 · Notes
Gas
Five hundred grains start huddled in the top-left. There is exactly one way to be that crowded. Once they move, the number of arrangements compatible with what you see climbs astronomically — and stays there.
Mix
Red top, blue bottom. There is no membrane between them. Each collision is reversible in principle; the bulk story is not. You cannot un-stir coffee, and the meter explains why.
Heat
Fast particles on the left, slow on the right. Collisions trade momentum, never destroy it. The thermal gradient flattens — same total energy, just spread evenly across degrees of freedom you can't see.
Brush
Click and drag inside the box. The cursor pushes particles outward like a stiff little wind. Try to sweep them back where they came from. Watch the meter sink, then climb again the instant you let go.

How the meter works

§ 05 · Method

Divide the box into a coarse grid of cells. Two arrangements are indistinguishable to the eye if every cell holds the same count — that is the macrostate. Boltzmann counted how many microstates (which-particle-is-where) collapse to each macrostate, then took the logarithm.

For occupancies ni with N particles total, the count of microstates is W = N! / ∏ ni!. The number on the right side of the bar is log10 W. A neat corner pile has W = 1 (everyone in one cell) so S = 0. A perfectly even spread maximises S at N · log10(number of cells). Your brush pushes the dust toward small W; thermodynamics pushes back, ruthlessly, by arithmetic alone.

Walls are elastic. Two-body collisions are elastic and momentum-conserving via a uniform spatial hash — the heat-flow mode equilibrates because of them, not in spite of them.