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To reach a deeper understanding of fluid interfaces it is necessary toidentify a meaningful coarse-graining length that separates intrinsicfluctuations from capillary ones, given the lack of a proper statisticalmechanical definition of the latter. Here, with the help of unsupervisedlearning techniques, we introduce a new length scale based on the local densityof the fluid. This length scale follows a scaling law that diverges more mildlythan the bulk correlation length upon approaching the critical point. Thisallows to distinguish regimes of correlated and uncorrelated capillary wavesfrom that of intrinsic fluctuations.

Structure and scaling laws of liquid/vapor interfaces close to the critical point