To complete our ontological interpretation of quantum theory we have t
o conclude a treatment of quantum statistical mechanics. The basic con
cepts in the ontological approach are the particle and the wave functi
on. The density matrix cannot play a fundamental role here. Therefore
quantum statistical mechanics will require a further statistical distr
ibution over wave functions in addition to the distribution of particl
es that have a specified wave function. Ultimately the wave function o
f the universe will be required, but we show that if the universe in n
ot in thermodynamic equilibrium then it can be treated in terms of wea
kly interacting large scale constituents that are very nearly independ
ent of each other. In this way we obtain the same results as those of
the usual approach within the framework of the ontological interpretat
ion.