  We show that for cubic scalar field theories in five and more spacetime
dimensions, and for the $T = 0$ limit of the Caldeira-Leggett model, the
quantum master equation for long-wavelength modes initially unentangled from
short-distance modes, and at second order in perturbation theory, contains
divergences in the non-Hamiltonian terms. These divergences ensure that the
equations of motion for expectation values of composite operators closes on
expectation values of renormalized operators. Along the way we show that
initial "jolt" singularities which occur in the equations of motion for
operators linear in the fundamental variables persist for quadratic operators,
and are removed if one chooses an initial state projected onto low energies,
following the Born-Oppenheimer approximation.
