  The solution to nonlinear Fokker-Planck equation is constructed in terms of
the minimal Markov semigroup generated by the equation. The semigroup is
obtained by a purely functional analytical method via Hille-Yosida theorem. The
existence of the positive invariant measure with density is established and a
weak form of Foguel alternative proven. We show the equivalence among
self-adjoint of the elliptic operator, time-reversibility, and zero entropy
production rate of the stationary diffusion process. A thermodynamic theory for
diffusion processes emerges.
