A system ofNtwo‐dimensional vortices interacting in a bounded region can be described by the statistics of the coordinates of the vortices or by the statistics of the Fourier coefficients of the vorticity field. It is shown that both descriptions give equivalent results. A high energy expression for the probability distribution function of the Fourier coefficients is derived and shown to be non‐Gaussian; it has at least two, and in some cases a continuum of, equal height maximum points corresponding to distinct, but equally probable, equilibrium states. Other stationary points previously thought to be metastable states are shown to be saddle points of the distribution function and hence unstable.