Relative entropy in Kac's model
= Relative entropy in Kac's model
{title2=$H_N(F)=\int F\log(F/\gamma_N)$}
Use $\gamma_N=(2\pi)^{-N/2}e^{-|v|^2/2}$ as the reference probability density. The <relative entropy> is nonnegative by writing $F=\gamma_Nu$ and integrating $u\log u-u+1$. Its expansion is $\int F\log F+(N/2)\log(2\pi)+(1/2)\int|v|^2F$. Equality holds only at $F=\gamma_N$, whereas other radial densities may still be stationary for the <Kac master equation>.