Minimum Kullback entropy approach to the Fokker-Planck equation

We consider a minimum Kullback entropy approach to determine approximate, time-dependent solutions to the $N$-dimensional Fokker-Planck (FP) equation. It is shown that the ensuing approximate solutions to the FP equation can be derived from a variational principle. We prove that the functional relation between the time derivative of the entropy, on the one hand, and the approximate (time-dependent) distribution functions, on the other, has the same form as that corresponding to exact solutions to the FP equation. Other properties of the approximate Kullback solutions and some particular examples are also discussed.