Robust asymptotic entanglement under multipartite collective dephasing

We derive an analytic solution for the ensemble-averaged collective dephasing dynamics of $N$ noninteracting atoms in a fluctuating homogeneous external field. The obtained Kraus map is used to specify families of states whose entanglement properties are preserved at all times under arbitrary field orientations, even for states undergoing incoherent evolution. Our results apply to arbitrary spectral distributions of the field fluctuations.