  We describe conditions on non-gradient drift diffusion Fokker-Planck
equations for its solutions to converge to equilibrium with a uniform
exponential rate in Wasserstein distance. This asymptotic behaviour is related
to a functional inequality, which links the distance with its dissipation and
ensures a spectral gap in Wasserstein distance. We give practical criteria for
this inequality and compare it to classical ones. The key point is to quantify
the contribution of the diffusion term to the rate of convergence, which to our
knowledge is a novelty.
