= -\BoltCons T \lim _{n \to 0}
        \frac{\partial}{\partial n} \ln Z_{1+n} \, ,\end{aligned}$$ where

$$\begin{aligned}
\label{EQ:ReplPart}
    Z_{1+n} &\equiv& \sum_{\RealDiso}
            \frac{\Big(\frac{\LinkDens \Volu_0}{2\PartNumb \LinkPote_0}\Big)^{\LinkNumb}}
            { \LinkNumb !} Z_{\RealDiso}(\Volu_0) Z_{\RealDiso}(\Volu)^n \nonumber\\
        &=& \PartitionLiquid(\Volu_0)\PartitionLiquid(\Volu)^n         \lthal \exp \Big(\frac{\LinkDens \Volu_0}
            {2\PartNumb \LinkPote_0}             \sum_{i\ne j}^{\PartNumb} \ReplProd
            \LinkPote  \big(
            \vert \PartPosi_{i}\REPa - \PartPosi_{j}\REPa \vert
            \big)\Big)\rthal_{1+n}^{\HamiExcl} .\end{aligned}$$

Notice that, here, the preparation state (i.e., $0^{\textrm{th}}$ replica) has a fixed volume $\Volu_0$ because, for convenience, we have assumed that the linking process was undertaken instantaneously in a liquid state of fixed volume and thus the pressure is fluctuating, whereas the measurement states (replicas $1$ through $n$) are put in a fixed-pressure $\Pres$ environment, the volume $\Volu$ of which is allowed to fluctuate. In the latter parts of the paper we shall set the pressure $\Pres$ to be the average pressure measured in the preparation state at volume $\Volu_0$. In particular, for a given volume of the liquid state in which the links are made, the average pressure is given by $$\begin{aligned}
    \Pres = - \frac{\partial \FLiquid (\Volu_0)}{\partial \Volu_0}
                    \Big\vert_{T} \, ,\end{aligned}$$ where we have introduced the Helmholtz free energy of the unlinked liquid $\FLiquid (\Volu_0) \equiv - \BoltCons T \ln \PartitionLiquid (\Volu_0)$. We suppose that the excluded-volume interactions are so 