Where does quantum mechanics part ways with classical mechanics? How doesquantum randomness differ fundamentally from classical randomness? We cannotfully explain how the theories differ until we can derive them within a singleaxiomatic framework, allowing an unambiguous account of how one theory is thelimit of the other. Here we derive nonrelativistic quantum mechanics andclassical statistical mechanics within a common framework. The common axiomsinclude conservation of average energy and conservation of probability current.But two axioms distinguish quantum mechanics from classical statisticalmechanics: an "ontic extension" defines a nonseparable (global) random variablethat generates physical correlations, and an "epistemic restriction" constrainsallowed phase space distributions. The ontic extension and epistemicrestriction, with strength on the order of Planck's constant, imply quantumentanglement and uncertainty relations. This framework suggests that the wavefunction is epistemic, yet it does not provide an ontic dynamics for individualsystems.
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