  In this paper, we study the long-time behaviour of solutions to the
Vlasov-Fokker-Planck equation where the confining potential is non-convex. This
is a nonlocal nonlinear partial differential equation describing the time
evolution of the probability distribution of a particle moving under the
influence of a non-convex potential, an interaction potential, a friction force
and a stochastic force. Using the free-energy approach, we show that under
suitable assumptions solutions of the Vlasov-Fokker-Planck equation converge to
an invariant probability.
