We have also used the flexibility of DoSPT to separately study the entropy of the first water layer (1WL) close to the metal surface as well as the entropy of the other water molecules comprising the interfacial bulk-like water layer (IBL), see the rough illustration in Figure . The division was made based on the ρ(z) structure. More precisely, the 1WL was defined as the region between the metal surface at z = 0 and the dip in ρ(z) at z ≈ 4 Å after the first density peak for Au and Ag and after the second peak for Pd, Pt, and Rh. Hence, the 1WL corresponds to an interfacial region where the water molecules have a preferential orientation and higher density as compared to bulk water. The IBL was considered to extend from the dip up to the onset of the lv interface (at z ≈ 15 Å), which was estimated by fitting a Gaussian function to the tail of ρ(z) and considering only those water molecules that were at least one full-width at half maximum (FWHM) distance away from the fit function center value. Because the water molecules are free to exchange positions between 1WL, IBL, and vapor regions, the division of molecules to these groups is not unique and only qualitative analysis of the entropy was possible. To this end, we chose to track which molecules were located within the 1WL and IBL for more than 80 % of the simulation time, and computed the 1WL and IBL entropies accordingly. The influence of the residence percentage on the entropies was preliminarily checked, and we observed that the 50-80 % criterion lead to very similar interfacial entropies. For details, see Supplementary material Table .