  The local pressure tensor is non-unique, a fact which has generated confusion
and debate in the seventy years since the seminal work by Irving Kirkwood. This
non-uniqueness is normally attributed to the interaction path between
molecules, especially in the interfacial-science community. In this work we
reframe this discussion of non-uniqueness in terms of the location, or
reference frame, used to measure the pressure. By using a general mathematical
description of the liquid-vapour interface, we obtain a reference frame that
moves with the interface through time, providing a new insight into the
pressure. We compare this instantaneous moving reference frame with the fixed
Eulerian one. Through this process, we show the requirement that normal
pressure balance at the moving surface is satisfied by surface fluxes, however
an additional corrective term based on surface curvature is required for the
average pressure in a volume. We make the case that a focus on the path of
integration is the cause of much of the confusion in the literature. Using an
explicit reference frame with a more general derivation of pressure clarifies
some of the issues of uniqueness in the pressure tensor and provides a pressure
tensor which is defined at any instant in time and valid away from
thermodynamic equilibrium.
