The Importance of Equilibrium

By equilibrium, I mean that certain statistical macroscopic properties of the system don't change in time. Even as microscopically the system could be all over the place and constantly changing. So if you were trying to track that one molecule, that's never an equilibrium. But if you're trying to track something like the density of molecules in any one region of space, then that shows some initial transient and then settles down into a near equilibrium state.