  Inhomogeneous fluids exhibit physical properties that are neither uniform nor
isotropic. The pressure tensor is a case in point, key to the mechanical
description of the interfacial region. Kirkwood and Buff, and later Irving and
Kirkwood, obtained a formal treatment based on the analysis of the pressure
across a planar surface [J.G. Kirkwood and F.P. Buff, J. Chem. Phys., 17(3),
(1949), J.H. Irving and J.G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We
propose a generalisation of Irving and Kirkwood's argument to fluctuating,
non-planar surfaces and obtain an expression for the pressure tensor that is
not smeared by thermal fluctuations at the molecular scale and corresponding
capillary waves [F.P. Buff, R.A. Lovett, and F.H. Stillinger, Jr., Phys. Rev.
Lett. 15, 621 (1965)]. We observe the emergence of surface tension, defined as
an excess tangential stress, acting exactly across the dividing surface at the
sharpest molecular resolution. The new statistical mechanical expressions
extend current treatments to fluctuating inhomogeneous systems far from
equilibrium.

Statistical Mechanics