"When an isolated system is left alone long enough, it evolves to thermal equilibrium. Equilibrium is not one particular microstate. Rather, it's that probability distribution of microstates having the greatest possible disorder allowed by the physical constraints on the system."
Many of the ideas in thermodynamics leave you with a sense of wondering how anything exciting can happen if a system is at equilibrium. However if you study a subsystem such as a single molecule the fluctuations that occur can represent a distribution of states, of which some will be high energy.
This leaves us with an idea that, at equilibrium, the total energy does not fluctuate because there are no more inputs into the system. However energy can still be transferred within and between subsystems at equilibrium.