  This paper is concerned with finding Fokker-Planck equations in
$\mathbb{R}^d$ with the fastest exponential decay towards a given equilibrium.
For a prescribed, anisotropic Gaussian we determine a non-symmetric
Fokker-Planck equation with linear drift that shows the highest exponential
decay rate for the convergence of its solutions towards equilibrium. At the
same time it has to allow for a decay estimate with a multiplicative constant
arbitrarily close to its infimum. Such an optimal Fokker-Planck equation is
constructed explicitly with a diffusion matrix of rank one, hence being
hypocoercive. In an $L^2$-analysis, we find that the maximum decay rate equals
the maximum eigenvalue of the inverse covariance matrix, and that the infimum
of the attainable multiplicative constant is 1, corresponding to the
high-rotational limit in the Fokker-Planck drift.
