Equipartition for a homogeneous potential
= Equipartition for a homogeneous potential
{title2=$\langle A|x|^s\rangle=k_BT/s$}
For a classical canonical coordinate with confining <potential energy> $U=A|x|^s$, $A>0$ and $s>0$, <integration by parts> in the <Boltzmann distribution> gives $\langle xU'(x)\rangle=k_BT$. Homogeneity then gives $\langle U\rangle=k_BT/s$. The usual quadratic contribution $k_BT/2$ is the special case $s=2$.