  We discuss the kinetic theory of stellar systems and two-dimensional vortices
and stress their analogies. We recall the derivation of the Landau and
Lenard-Balescu equations from the Klimontovich formalism. These equations take
into account two-body correlations and are valid at the order $1/N$, where $N$
is the number of particles in the system. They have the structure of a
Fokker-Planck equation involving a diffusion term and a drift term. The
systematic drift of a vortex is the counterpart of the dynamical friction
experienced by a star. At equilibrium, the diffusion and the drift terms
balance each other establishing the Boltzmann distribution of statistical
mechanics. We discuss the problem of kinetic blocking in certain cases and how
it can be solved at the order $1/N^2$ by the consideration of three-body
correlations. We also consider the behavior of the system close to the critical
point following a recent suggestion by Hamilton and Heinemann (2023). We
present a simple calculation, valid for spatially homogeneous systems with
long-range interactions described by the Cauchy distribution, showing how the
consideration of the Landau modes regularizes the divergence of the friction by
polarization at the critical point.
