+ U_{\text{eq}} + U_{\text{harm}}\right)\right]\nonumber\\
+ &=&
+ \exp(-\beta U_{\text{eq}})\beta^{-3N}
+ \LARGE(\int\prod_{{\bf R}}d\bar{{\bf u}}({\bf R})d\bar{{\bf P}}({\bf R})
+ \nonumber\\
+ &&\times \exp\left[
+ -\sum\frac{1}{2M}{\bf P}({\bf R})^2
+ -\frac{1}{4}\sum
+ [\bar{u}_{\mu}({\bf R})-\bar{u}_{\mu}({\bf R'})]
+ \Phi_{\mu v}({\bf R}-{\bf R'})
+ [\bar{u}_v({\bf R})-\bar{u}_v({\bf R'})]
+ \right]\LARGE)\nonumber
+ \end{eqnarray}
+ \[
+ \Rightarrow w=-\frac{1}{V}\frac{\partial}{\partial \beta}
+ ln\left((\exp(-\beta U_{\text{eq}})\beta^{-3N} \times \text{const}
+ \right)
+ =\frac{U_{\text{eq}}}{V}+3\frac{N}{V}k_{\text{B}}T
+ =u_{\text{eq}}+3nk_{\text{B}}T
+ \]
+ \[
+ \Rightarrow
+ c_{\text{V}}=\frac{\partial w}{\partial T}=3nk_{\text{B}}