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Collapse and evaporation of a canonical self-gravitating gas

We review the out-of-equilibrium properties of a self-gravitating gas of particles in the presence of a strong friction and a random force (canonical gas). We assume a bare diffusion coefficient of the form $D(ρ)=Tρ^{1/n}$, where $ρ$ is the local particle density, so that the equation of state is $P(ρ)=D(ρ)ρ$. Depending on the spatial dimension $d$, the index $n$, the temperature $T$, and whether the system is confined to a finite box or not, the system can reach an equilibrium state, collapse or evaporate. This article focuses on the latter cases, presenting a complete dynamical phase diagram of the system.