From Jupiter's great red spot to the structure of galaxies: Statistical mechanics of two-dimensional vortices and stellar systems

The statistical mechanics of two-dimensional vortices and stellar systems both at equilibrium and out of equilibrium are discussed, with emphasis on the analogies (and on the differences) between these two systems. Limitations of statistical theory and problems posed by the long-range nature of the interactions are described in detail. Special attention is devoted to the problem of "incomplete relaxation" and, in the case of stellar systems, to the "gravothermal catastrophe." The relaxation toward equilibrium, possibly restricted to a "maximum entropy bubble," is described with the aid of a maximum entropy production principle (MEPP). The relation with Fokker-Planck equations is made explicit and the structure of the diffusion current analyzed in terms of a pure diffusion compensated by an appropriate friction or a drift.