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Here are a few ideas I have about the so-called heat-death hypothesis.

First, if we take the wikipedia entry as a description, it's inherently false. It suggests that the universe reaches maximum entropy, which implies that the second law of thermodynamics is violated. So, obviously maximum entropy will never be reached. In fact the real model suggests a limiting function that keeps coming closer but in fact never reaches it.

Or could it?

If we take into account Zeno's paradox, then things like this happen all the time. We know from calculus that theoretically I can never move exactly from one space to another due to a limiting process, but in fact this is violated all the time in nature by casual observation. In fact, if this was impossible I could not move anywhere at all. So does this mean that the second law can be violated, or that Zeno's paradox is somehow fundamentally flawed?

Other research seems to imply an 'entropy gap' which inevitably will push the system away from equilibrium. Can someone explain how that would form? I couldn't find much material on it.