Isothermal-isobaric partition function
= Isothermal-isobaric partition function
{title2=$\Delta=\int_0^\infty Z(N,V,T)e^{-\beta PV}\,dV$}
Integrating a <canonical partition function> over <volume> gives the displayed continuous-volume normalization. For a temperature-independent measure and Hamiltonian, $-\partial_\beta\ln\Delta=\langle E+PV\rangle$. Multiplying by a volume-independent prefactor leaves normalized volume probabilities unchanged, but a temperature-dependent prefactor changes this derivative.