In addition to the explicit dependence of N w in Eq. ( ), we note a subtle finite-size effect based on our heterogeneous system construction. Briefly, while the water molecule being "added" to the system has access to the full volume of the simulation cell, as λ increases, it is primarily in the vicinity of preexisting water in the system. Because the volume of preexisting water scales with N w but the total volume of the simulation cell remains unchanged, the ratio of water to system volume changes with N w . The leading-order contribution to the free energy of the newly added water will simply scale with the water volume (see Supporting