It has been observed empirically that two dimensional vortices tend to
cluster forming a giant vortex. To account for this observation Onsager
introduced a concept of negative absolute temperature in equilibrium
statistical mechanics. In this Letter we will show that in the thermodynamic
limit a system of interacting vortices does not relax to the thermodynamic
equilibrium, but becomes trapped in a non-equilibrium stationary state. We will
show that the vortex distribution in this non-equilibrium stationary state has
a characteristic core-halo structure, which can be predicted {\it a priori}.
All the theoretical results are compared with explicit molecular dynamics
simulations
