strong that the density fluctuations are suppressed, and the density of the unlinked liquid is just $\PartNumb/\Volu_0$. [^4] Thus, the mean-field value of Helmholtz free energy in the unlinked liquid state is $$\begin{aligned}
\label{EQ:FLiquid}
    \FLiquid (\Volu_0) &=& -\PartNumb \BoltCons T \ln \Volu_0
        +\frac{\ExclVolu \PartNumb^2}{2\Volu_0}.\end{aligned}$$ Therefore, the mean pressure in the unlinked liquid state is given by $$\begin{aligned}
\label{EQ:AverPres}
    \Pres = \frac{\PartNumb \BoltCons   T}{\Volu_0}
        +\frac{\ExclVolu \PartNumb^2}{2\Volu_0^2},\end{aligned}$$ [[from which we can identify—by the standard way in which the second virial coefficient $B_2$ appears in the free energy of the equation of state for a fluid—that $B_2$ for the unlinked liquid is $\ExclVolu/2\BoltCons T$. Thus, without having actually performed a cluster expansion, we see that the Dirac delta-function interaction with coefficient $\ExclVolu$ indeed leads to a virial expansion with a suitable excluded volume, viz., $\ExclVolu/(\BoltCons T)$. ]{}]{} As mentioned above, we shall apply this pressure in the measurement states (described by $1^{\textrm{th}}$ through $n^{\textrm{th}}$ replicas), and let their volumes $\Volu$ fluctuate, in order to obtain an elastic free energy that can describe volume variations. In particular, by choosing the pressure $p$ to be exactly the mean pressure of the liquid state, we shall obtain an elastic free energy that takes the *state right 