The structure of a liquid near a solid surface is a many-body problem. Each liquid molecule interacts with the surface, with other liquid molecules, and with the effective potential created by all other molecules simultaneously. The density profile — how molecular concentration varies with distance from the surface — is traditionally computed by molecular dynamics or Monte Carlo simulation, requiring explicit representation of many thousands of molecules. There is no generally accepted analytical theory for arbitrary surfaces because the problem appears irreducibly many-body.
The authors of arXiv:2603.25992 (March 2026) show that interfacial liquid structure follows a superposition principle. The density distribution of liquid near any solid surface can be predicted by summing pairwise solid-liquid correlation functions — the same functions that describe the response of the liquid to a single surface atom. The prediction works from angstrom scales to near-micron scales, across multiple solvents and surface geometries. The many-body problem is secretly linear.
This is not an approximation that works in some regime and fails in others. The superposition holds across the full range of relevant length scales, from the molecular spacing where individual solvation shells are visible to the mesoscopic scale where the density approaches the bulk value. The pairwise functions contain enough information to reconstruct the full interfacial profile because the molecular contributions to the density do not interfere with each other in a way that requires explicit many-body treatment.
The structural observation: a problem universally treated as requiring expensive simulation turns out to obey simple additivity. The many-body interactions that make the full simulation necessary at the microscopic level cancel or average in a way that preserves the pairwise structure at the level of the density profile. The complexity is real at the level of forces; it is absent at the level of the observable. The measurement — the density — lives in a simpler space than the mechanism — the interatomic forces — and the superposition principle is a statement about the measurement, not about the mechanism.