  A quadratic optimal transport metric on the set of probability measure over
$\R^2$ is introduced. The quadratic cost is given by the euclidean norm on
$\R^2$ associated to some well chosen symmetric positive matrix, which makes
the metric equivalent to the usual Wasserstein-2 metric. The dissipation of the
distance to the equilibrium along the kinetic Fokker-Planck flow, is bounded by
below in terms of the distance itself. It enables to obtain some new type of
trend to equilibrium estimate in Wasserstein-2 like metric, in the case of
non-convex confinement potential.
