as the QoI, Q is simply the sum of Eq. \[eq:PEcoord\] and the low-fidelity simulation potential energy. For the pressure we use the virial expression (without the small ideal gas contribution as it is already present in the low-fidelity pressure): $$\label{eq:Pallvec}
P' = \frac{1}{3V}\sum_{i<j} \textbf{f}_{ij} \textbf{r}_{ij}$$ Because we examine cases of two-body central forces this can be simplified: $$\label{eq:Pall}
P' = \frac{1}{3V}\sum_{i<j} f(r_{ij})r_{ij}$$ and with the same motivations as above, we rewrite in terms of the coordination number, again with $k$ bins in separation distance: $$\label{eq:Pcoord}
P' = \frac{N}{2} \frac{1}{3V}\sum_k f(r_k)\cdot r \cdot c(r_k)$$

This quantity, added to the low-fidelity simulation pressure, provides Q in Eq. \[eq:perturbative\] for the QoI pressure.

Correction results
==================

Tables \[tbl:PE\] and \[tbl:P\] show full results for all physical conditions for potential energy and pressure, respectively. Figure \[fig:results\] compares columns $\Delta Q^{Sim}$ and $\Delta Q^{FUQ}$. All results here are calculated with respect to the LJ low-fidelity potential, except the rows marked with (H). Those cases use the low-fidelity hybrid LJ-Morse potential.

  Temp.   Potential   $Q_{LF}$   $Q_{HF}$   $Q_{LF} + \Delta Q^{FUQ}$   $\Delta Q^{Sim}$   $\Delta Q^{FUQ}$   $\Delta Q$ % Error
  ------- ----------- ---------- ---------- --------------------------- ------------------ ------------------ --------------------
  (K)     -                      -                                                                            
  300     Sine 1      -1.08      -1.28      -1.27                       -0.197             