There's also the question of heating up the coffee. Are you disentangling it from the air and entangling it with the hot particles below? It does not make sense

There's also the question of heating up the coffee. Are you disentangling it from the air and entangling it with the hot particles below? It does not make sense to equate equilibrium with entanglement. We have two systems that have been isolated from each other. Then they get together and get entangled. The number of states in which they have come to thermal equilibrium while entangled is far greater than the number in which they do not. They are being entangled, but that is just the process of putting the systems together, a necessary step in removing their isolationist tendencies, I would imagine. So entanglement is part of the process, but the classical notion of the evolution going to "more states" is still there. But going towards equilibrium is more general than isolationist --> entangled. Whatever your state psi is of the system, it is likely to evolve, if it can, into a state that belongs to a more numerous class.