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paper-machine comments on Hug the Query - Less Wrong
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A thermodynamic equilibrium would mean that the decreases in entropy would equal the increases. Since the decreases must be zero by the second law, the increases would also have to be zero. The laws of thermodynamics don't technically say that it has to increase, but there are things that you can't really prevent. If anything accelerates, it will emit gravitational waves, increasing entropy.
I mean that in order for the universe to be in a heat death state, that universe needs to be in thermodynamic equilibrium. You don't get that merely from the first and second laws.
For instance, the universe could expand. If it expands fast enough, the entropy associated with the heat death state could rise faster than its own entropy can increase, kicking it out of heat death. That's what I mean by needing a cosmological assumption.