  We derive the proper form of Virial theorem for a system of rotating
self-gravitating Brownian particles. We show that, in the two-dimensional case,
it takes a very simple form that can be used to obtain general results about
the dynamics of the system without being required to solve the
Smoluchowski-Poisson system explicitly. We also develop the analogy between
self-gravitating systems and two-dimensional point vortices and derive a
Virial-like relation for the vortex system.
