= Kac entropy production
{c}
{title2=$D_N(F)=-\frac d{dt}H_N(F)\geq0$}
= Kac entropy dissipation
{c}
{synonym}
For the <Kac master equation> and finite differentiable entropy, mass and energy conservation remove the non-logarithmic entropy terms. Symmetrizing each pair rotation then gives $D_N(F)=[2\pi(N-1)]^{-1}\sum_{i<j}\int\int(F\circ R_{ij,\theta}-F)\log((F\circ R_{ij,\theta})/F)\,dv\,d\theta$. The integrand is nonnegative by monotonicity of the logarithm, with the usual extended convention at zeros. Zero dissipation corresponds to radiality; it need not imply zero relative entropy.
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