Thermodynamic and statistical mechanical descriptions of non-uniform fluids

It is shown that the external field methods of equilibrium statistical mechanics have the same structure as thermodynamics. This means that thermodynamic definitions of physical properties can be converted directly into molecular descriptions. This is illustrated by identifying the local pressure in a non-uniform fluid. This means that molecular constraints on thermodynamics can be found by giving a thermodynamic interpretation to molecular results. This is illustrated by providing a molecular picture of van der Waalsʹ density gradient expansion.