  We deduce a class of non-Markovian completely positive master equations which
describe a system in a composite bipartite environment, consisting of a
Markovian reservoir and additional stationary unobserved degrees of freedom
that modulate the dissipative coupling. The entanglement-induced memory effects
can persist for arbitrary long times and affect the relaxation to equilibrium,
as well as induce corrections to the quantum-regression theorem. By considering
the extra degrees of freedom as a discrete manifold of energy levels, strong
non-exponential behavior can arise, as for example power law and stretched
exponential decays.
