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Epictetus comments on Open Thread, Feb. 2 - Feb 8, 2015 - Less Wrong Discussion
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The lesson is that statistical methods are superfluous if you know everything with certainty. It's worth noting that classical mechanics is completely symmetric with respect to time (does not have a distinguished "arrow of time"), whereas thermodynamics has a definite arrow of time. You run into problems if you assume that everything behaves classically and try to apply thermodynamic notions.
Landau and Lifshitz's Statistical Physics has some discussion of issues with entropy.
I understand what you're saying and I agree. Though it's worth mentioning that the 'arrow of time' in thermodynamics actually doesn't exist for closed, reversible systems.