Statistical mechanics of a self gravitating gas

Abstract

Classical point particles interacting via a two-body Newtonian potential cannot be described by the Gibbs-Boltzmann statistics, because of fatal divergences at short distances of the partition function. The assumption of uniform filling of the phase space in the course of time must be replaced by the one of spreading in phase space going forever. What replaces the Gibbs-Boltzmann statistics then are asymptotic diffusion-like laws for this spreading process, where the time enters as a scaling parameter. Another possible description of systems of particles with long range interactions is the continuum Vlasov mean field equation. It is argued that solutions of these Vlasov-Newton equations have finite time singularities with spherical symmetry, and focusing of the energy with no mass, like focusing NLS in 3D.