You can also throw in the Bohmians, since you can express at least non-relativistic QM in purely deterministic terms akin to stat mech (it's purely classical un

You can also throw in the Bohmians, since you can express at least non-relativistic QM in purely deterministic terms akin to stat mech (it's purely classical uncertainty about your position in configuration space, and there are stat-mech-like arguments for why that distribution should be very close to the Born distribution). Personally I don't know all that many physicists who think the universe is fundamentally stochastic (I work in quantum information).