= Spin-degeneracy shift of a charge step
{title2=$\mu_{1/2}=\epsilon-k_BT\ln2,\quad\mu_{3/2}=\epsilon+U+k_BT\ln2$}
Near the first addition threshold of a repulsive single-orbital defect, the empty and singly occupied grand weights are 1 and $2e^{\beta(\mu-\epsilon)}$. Equal weights occur at $\mu=\epsilon-k_BT\ln2$. Near the second threshold, the single/double aggregate weights are in ratio $2:e^{\beta(\mu-\epsilon-U)}$, giving half-step position $\epsilon+U+k_BT\ln2$. These are entropic finite-temperature shifts, which vanish in <energy> units as $T\to0$. They must still be retained when evaluating statistics exactly at an unshifted degeneracy point.
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