So, if the surrounding air is 60°, then an 80° pool will shed heat energy twice as fast as a 70° pool. This is why coffee/tea/soup will be hot for a little while, but tepid for a long time; it cools faster when it’s hotter. Since you lose more heat energy from a hot pool than from a cool pool, the most efficient thing you can do is keep the temperature as low as possible for as long as possible. The same equation describes the random motion of particles. If is either the density of “beads” or the probability of finding a bead at a particular place (if the movement of the beads is independent, then these two situations are interchangeable), then once again the diffusion equation describes how the bead density changes over time. You can actually derive useful math from it, which is a damn sight better than most science metaphors (E.g., “space is like a rubber sheet” is not useful for actual astrophysicists). In very much the same way that a concentrated collection of beads will spread themselves uniformly, hot things will lose heat energy to the surrounding cooler environment.
