= Heat-capacity activation estimate
{title2=$\Delta/k_B=\ln[C(T_2)/C(T_1)]/(T_1^{-1}-T_2^{-1})$}
For gapped excitations with $C(T)\simeq A\exp[-\Delta/(k_BT)]$ and approximately constant prefactor, two <heat capacity> measurements at $T_2>T_1$ give the displayed activation-energy estimate. A more general prefactor $AT^p$ changes its numerator to $\ln[C(T_2)/C(T_1)]-p\ln(T_2/T_1)$. The two-point estimate measures an effective exponential scale; it does not independently determine the prefactor or establish a detailed excitation <density of states>.
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