  In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has
been shown that the mean particle-particle interaction across an ideal surface
that divides a system into two parts, can be employed to estimate the size
dependence for the thermodynamic accuracy of the system. In this work we
propose its application to systems with finite range interactions that models a
dense quantum gases and derive an approximate size-dependence scaling law. In
addition, we show that the application of the criterion is equivalent to the
determination of a free energy response to a perturbation. The latter result
confirms the complementarity of the criterion to other estimates of finite-size
effects based on direct simulations and empirical structure or energy
convergence criteria.
