  The goal of this work is to find the sharp rate of convergence to equilibrium
under the quadratic Fisher information functional for solutions to
Fokker-Planck equations governed by a constant drift term and a constant, yet
possibly degenerate, diffusion matrix. A key ingredient in our investigation is
a recent work of Arnold, Signorello, and Schmeiser, where the $L^2$-propagator
norm of such Fokker-Planck equations was shown to be identical to the
propagator norm of a finite dimensional ODE which is determined by matrices
that are intimately connected to those appearing in the associated
Fokker-Planck equations.
