Physics
Heat flow, gases and statistical energy distributions.
high energy is possible, just exponentially rare
At temperature T a state of energy E is weighted by e^(−E/kT). Metropolis sampling reproduces the distribution with a simple accept/reject rule.
each cell drifts toward the average of its neighbours
Heat flows down temperature gradients at a rate set by the Laplacian. The explicit grid update is four lines of code, and is stable only if αΔt/Δx² ≤ ¼.
pressure is just particles bouncing off walls
Temperature is average kinetic energy and pressure is momentum delivered to the walls. Bounce point particles in a box and PV = NkT falls out.