A comparison is made between the traditional stress-tenser based approach t
o the local pressure in a curved liquid-vapor interface and a novel purely
thermodynamic approach. While both approaches are equivalent for planar int
erfaces, the stress-tenser based approach becomes ambiguous on a molecular
scale for curved interfaces. We illustrate how the value of the surface ten
sion and the location of the surface of tension can be obtained from the th
ermodynamic approach when the pressure profile of a spherical interface is
computed within a molecular dynamics simulation.