  How physical systems approach hydrodynamic behavior is governed by the decay
of nonhydrodynamic modes. Here, we start from a relativistic kinetic theory
that encodes relaxation mechanisms governed by different timescales thus
sharing essential features of generic weakly coupled nonequilib- rium systems.
By analytically solving for the retarded correlation functions, we clarify how
branch cuts arise generically from noncollective particle excitations, how they
interface with poles arising from collective hydrodynamic excitations, and to
what extent the appearance of poles remains at best an ambiguous signature for
the onset of fluid dynamic behavior. We observe that processes that are slower
than the hydrodynamic relaxation timescale can make a system that has already
reached fluid dynamic behavior to fall out of hydrodynamics at late times. In
addition, the analytical control over this model allows us to explicitly
demonstrate how the hydrodynamic gradient expansion of the correlation
functions can be Borel resummed such that the full nonperturbative information
is recovered using perturbative input only.
