Enthalpy fluctuation formula ($C_P=\mathrm{Var}(H)/(k_B{T}^2)$)

With temperature-independent microstate enthalpies and measure, differentiating the normalized weight $e^{-\beta H}/\Delta$ gives ${\partial }_{\beta }⟨H⟩=-\mathrm{Var}(H)$. Since $d\beta /dT=-1/(k_B{T}^2)$, the displayed response follows. A stable finite-system equilibrium distribution therefore has nonnegative heat capacity at constant pressure in this setting.