  Colloidal bodies of irregular shape rotate as they descend under gravity in
solution. This rotational response provides a means of bringing a dispersion of
identical bodies into a synchronized rotation with the same orientation using
programmed forcing. We use the notion of statistical entropy to derive bounds
on the rate of synchronization. These bounds apply generally to dynamical
systems with stable periodic motion with a phase $\phi(t)$, when subjected to
an impulsive perturbation. The impulse causes a change of phase expressible as
a phase map $\psi(\phi)$. We derive an upper limit on the average change of
entropy $\left<\Delta H\right>$ in terms of this phase map; when this limit is
negative, alignment must occur. For systems that have achieved a low entropy,
the $\left<\Delta H\right>$ approaches this upper limit.
