The inclusion of the drift force in the dynamics of AdSoS is essential to prevent the occurrence of density artifacts. As discussed previously , this force compensates on average for the thermodynamic driving force associated with a heterogeneous pressure in the system, which results from the fact that the pressure in a solvent region at scaling s is given by P(s) = s -3 P * . This pressure heterogeneity is necessary because the pressure s -3 P * is the one that leads to the correct solvent number density ρ(s) = s -3 ρ * . Note that this compensation only holds in the limit of a sufficiently large number of molecules and of sufficiently low s-gradients in the system.