Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a $N$-dimensional Brownian motion) is injected in the system, we prove that the asymptotic rate of convergence is maximized by a non-reversible hypoelliptic one.
"Optimal linear drift for the speed of convergence of an hypoelliptic diffusion." Electron. Commun. Probab. 21 1 - 14, 2016. https://doi.org/10.1214/16-ECP25