Logarithmic Sobolev inequality
= Logarithmic Sobolev inequality
{title2=$\operatorname{Ent}_\mu(g^2)\leq c_{\mathrm{LS}}\mathcal E_\mu(g)$}
{wiki}
Here $\operatorname{Ent}_\mu(h)=\int h\log h\,d\mu-(\int h\,d\mu)\log\int h\,d\mu$ for a probability measure. The coefficient depends on the normalization of the energy. With the joint energy $-\langle Lg,g\rangle$ for $L=D^2-xD$, standard Gaussian measure has optimal constant two.
// Target: analysis.bigb