Entropy dissipation identity for Ornstein-Uhlenbeck flow
= Entropy dissipation identity for Ornstein-Uhlenbeck flow
{title2=$\frac d{dt}H(f_t\mid\gamma)=-I(f_t\mid\gamma)$}
For a sufficiently regular unit-mass solution, the <Ornstein-Uhlenbeck Fokker-Planck equation> is $\partial_tf=\nabla\cdot(f\nabla\log(f/\gamma))$. <Integration by parts> proves the displayed identity. Consequently <relative entropy> decreases, and its dissipation is <relative Fisher information>.