It seems as though a bunch of water is a good place to store heat energy, but the more time something spends being hot, the more energy it drains into everything around it.

The second derivative, , is a way to describe how a function is curving.

If the temperature of the pool and the air above it are equal, then the amount of heat that flows out of the pool is equal to the amount that flows in.

But if the pool is hotter, then more “beads” will randomly roll out than randomly roll in.

It’s all well and good to talk about how heat beads randomly walk around inside of a material, but if that material isn’t uniform or has an edge, then suddenly the math gets remarkably nasty.