  We investigate the problem of what evolutions an open quantum system
described by a time-local Master equation can undergo with universal coherent
controls. A series of conditions are given which exclude channels from being
reachable by any unitary controls, assuming that the coupling to the
environment is not being modified. These conditions primarily arise by defining
decay rates for the generator of the dynamics of the open system, and then
showing that controlling the system can only make these rates more isotropic.
This forms a series of constraints on the shape and non-unitality of allowed
evolutions, as well as an expression for the time required to reach a given
goal. We give numerical examples of the usefulness of these criteria, and
explore some similarities they have with quantum thermodynamics.
