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I bet the zero point fluctuation motion of the last gear dwarfs the deterministic motion.

The word you're looking for is "thermal." The bulk of the gear behaves completely classically at this temperature.

I think you are right in the sense that at room temperature, thermal fluctuations dominate.

Better stated, my point is that if the entire assembly is at absolute zero, the quantum fluctuations in the final gear are much greater than the deterministic motion associated with one revolution of the first gear.

If this entire assembly is at absolute zero, something is very wrong in the universe.

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