Equilibrium

Equilibrium is the settled state a system reaches when the differences in chemical potential within it have closed. At the macroscopic level we recognize it by what we no longer see: nothing appears to be changing further. The liquid in the beaker holds its color. The temperatures have met. The scale reads the same minute after minute. Whatever was going on has finished, at least as far as our instruments can say.

Equilibrium is best understood by pairing it with its opposite. Where there is a difference in chemical potential between two parts of a system, change tends to occur, and the moving closes the difference. Water runs from the high reservoir to the low. Heat moves from the hot piece of iron to the cold piece pressed against it. Salt spreads through the water it is dissolved in. As long as there is a difference, there is a tendency. When the difference reaches zero, the tendency reaches zero, and the change stops. That stopping is equilibrium.

Notice that the materials at equilibrium are not gone and they are not inert. They are simply at rest with respect to each other. The settled state is defined by the balance, not by any quality of the materials in isolation. Two cups of water at the same temperature are in thermal equilibrium with each other; neither is especially "still," but the difference between them is zero, and so nothing further moves. Equilibrium is a property of the system, not a property of any single material within it.

This is why equilibrium shows up so often as the destination of the universal process. Reactions run, state transitions occur, materials diffuse and relocate, and each of these is an instance of the same shape: a movement from a state of unbalanced potential to a state of balance. The process ends where the difference ends. Equilibrium is the quiet at the bottom of the hill. It is not nothing; it is everything finished.