Entropy convergence rate for Ornstein-Uhlenbeck flow
= Entropy convergence rate for Ornstein-Uhlenbeck flow
{title2=$H(f_t\mid\gamma)\leq e^{-2t}H(f_0\mid\gamma)$}
The inequality $H\leq I/2$ and the <entropy dissipation identity for Ornstein-Uhlenbeck flow> imply $H'\leq-2H$. An integrating factor proves the displayed estimate from initial entropy alone. <Pinsker's inequality> then gives $\|f_t-\gamma\|_1\leq\sqrt{2H(f_0\mid\gamma)}e^{-t}$.