Enthalpy fluctuation formula
= Enthalpy fluctuation formula
{title2=$C_P=\operatorname{Var}(H)/(k_BT^2)$}
With temperature-independent microstate enthalpies and measure, differentiating the normalized weight $e^{-\beta H}/\Delta$ gives $\partial_\beta\langle H\rangle=-\operatorname{Var}(H)$. Since $d\beta/dT=-1/(k_BT^2)$, the displayed response follows. A stable finite-system equilibrium distribution therefore has nonnegative <heat capacity at constant pressure> in this setting.