  It is long known that the Fokker-Planck equation with prescribed constant
coefficients of diffusion and linear friction describes the ensemble average of
the stochastic evolutions in velocity space of a Brownian test particle
immersed in a heat bath of fixed temperature. Apparently, it is not so well
known that the same partial differential equation, but now with constant
coefficients which are functionals of the solution itself rather than being
prescribed, describes the kinetic evolution (in the infinite particle limit) of
an isolated N-particle system with certain stochastic interactions. Here we
discuss in detail this recently discovered interpretation.
