Hard-wall correction to harmonic equipartition
= Hard-wall correction to harmonic equipartition
If $a\gg k_BT$, the wall is thermally inaccessible and $\langle E\rangle\sim2k_BT$, as four quadratic terms predict. If $a\ll k_BT$, the spatial distribution is nearly uniform in the disk and
$$
\langle E\rangle
=k_BT+\frac{\kappa R^2}{4}+O\left(\frac{\kappa^2R^4}{k_BT}\right),
$$
so only the two kinetic quadratic terms contribute at leading order.