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In order to provide a formally correct thermodynamical description ofinhomogeneous fluids valid on all length scales down to the classical limit wepostulate that all extensive quantities have locally extensive analogues. Wederive local thermodynamic relations for the canonical and isothermal- isobaricensembles without limitations with respect to the nature of intermolecularinteractions. The inhomogeneity of the system is shown to result in twodistinct entropic contributions. The intrinsic contribution is due the specificdistribution of local environments experienced by a single molecule while theextrinsic one originates exclusively from the local variation of the densityfrom its bulk value.

Exact Generalization of Local Thermodynamics of Inhomogeneous Fluids to Arbitrary Spatial Scales