  We present a new derivation of the Onsager-Joyce-Montgomery (OJM) equilibrium
statistical theory for point vortices on the plane, using the
Bogoliubov-Feynman inequality for the free energy, Gibbs entropy function and
Landau's approximation. This formulation links the heuristic OJM theory to the
modern variational mean field theories. Landau's approximation is the physical
counterpart of a large deviation result, which states that the maximum entropy
state does not only have maximal probability measure but overwhelmingly large
measure relative to other macrostates.
