  It has recently been shown, by application of statistical mechanical methods
to determine the canonical ensemble governing the equilibrium distribution of
operator initial values, that complex quantum field theory can emerge as a
statistical approximation to an underlying generalized quantum dynamics. This
result was obtained by an argument based on a Ward identity analogous to the
equipartition theorem of classical statistical mechanics. We construct here a
microcanonical ensemble which forms the basis of this canonical ensemble. This
construction enables us to define the microcanonical entropy and free energy of
the field configuration of the equilibrium distribution and to study the
stability of the canonical ensemble. We also study the algebraic structure of
the conserved generators from which the microcanonical and canonical ensembles
are constructed, and the flows they induce on the phase space.
