I'm having a hard time reconciling two ideas in physics. One is that systems tend towards the maximum amount of disorder, or "entropy always increases". And, when two systems are brought together they are likely to be found at the energy E* which maximizes the number of states of the combined system. However, it would appear that E* is not necessarily the minimum energy of the combined system. This is where I am hung up a bit. In other areas of physics, systems seem to always tend towards the least energy state. An electron cascading back to the ground state of a hydrogen atom, which is 13.6 eV, the state with the least energy, or largest negative bound energy. Or, the shape a soap film takes. Etc. Perhaps there is no conflict here, I guess it just struck me as strange.