A general relation is derived between the pressure tensor in an equilibrated inhomogeneous fluid and the direct correlation function. This relation reduces to the usual compressibility equation for a homogeneous fluid and is to be considered as the generalized compressibility equation. The equation provides a starting point for integral-equation theories and is useful in the rigorous kinetic theory of inhomogeneous fluids.

• Received 22 April 1993

DOI:https://doi.org/10.1103/PhysRevE.48.1819