I would really like to see the proof that it's impossible to design a reversible state machine that won't cycle. But even if you do prove that, you would also have to prove that if the laws of physics are reversible that the universe is reversible.
The current best theory and understanding of the evolution of the universe is that it will reach maximum entropy (heat death). There is no cycling when this happens. Can you cite what theory or new discovery you have come across that somehow challenges the heat death hypothesis?
