  Where does quantum mechanics part ways with classical mechanics? How does
quantum randomness differ fundamentally from classical randomness? We cannot
fully explain how the theories differ until we can derive them within a single
axiomatic framework, allowing an unambiguous account of how one theory is the
limit of the other. Here we derive nonrelativistic quantum mechanics and
classical statistical mechanics within a common framework. The common axioms
include conservation of average energy and conservation of probability current.
But two axioms distinguish quantum mechanics from classical statistical
mechanics: an "ontic extension" defines a nonseparable (global) random variable
that generates physical correlations, and an "epistemic restriction" constrains
allowed phase space distributions. The ontic extension and epistemic
restriction, with strength on the order of Planck's constant, imply quantum
entanglement and uncertainty relations. This framework suggests that the wave
function is epistemic, yet it does not provide an ontic dynamics for individual
systems.
