  We define an ensemble of projection operators, each of which has an exact
associated Nakajima-Zwanzig master equation for quantum open system evolution.
A mean field approximation for the memory kernels is introduced that yields,
for an optimally chosen projection operator, a completely determined
inhomogeneous master equation. Previous proofs of positivity and equilibration
are extended to these new inhomogeneous non-Markovian master equations. We
study a nitrogen vacancy center in diamond interacting with 13C impurities to
illustrate the method.
