If you know precisely the state of every water molecule in the system, there's no need for your finger to get burned. Just touch your finger to the cup whenever a slow-moving molecule is approaching, and remove it whenever a fast-moving molecule is approaching (Maxwell's demon).
Right, supposing you can have a macroscopic Maxwell's demon. So the claim is not that it is necessarily at absolute zero, but that it does not have a well-defined temperature, because you can choose it to behave (with respect to your finger) as if it were at any temperature you like. Is this what you are saying?
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