Entropy convergence rate for Ornstein-Uhlenbeck flow ($H(f_t\mid \gamma )\le e^{-2t}H(f_0\mid \gamma )$)

The inequality $H\le I/2$ and the entropy dissipation identity for Ornstein-Uhlenbeck flow imply $H^{\prime }\le -2H$. An integrating factor proves the displayed estimate from initial entropy alone. Pinsker's inequality then gives $\Vert f_t-\gamma {\Vert }_1\le \sqrt{2H(f_0\mid \gamma )}{e}^{-t}$.