The heat equation ∂u/∂t = α∇²u has an exact Green's function: G(x,t) = (4παt)^(−d/2) exp(−|x|²/(4αt)). An initial impulse (delta function) spreads as a Gaussian whose width grows as √(αt). Click on the canvas to add heat sources. Watch entropy increase as the distribution broadens.
G(x,t) = (4παt)^(−½) exp(−x²/(4αt)) in 1D | Entropy S(t) = ½ ln(4παet)