Nonequilibrium thermodynamics of an interface

Interfacial thermodynamics has deep ramifications in understanding the boundary conditions of transport theories. We present a formulation of local equilibrium for interfaces that extends the thermodynamics of the ``dividing surface,'' as introduced by Gibbs, to nonequilibrium settings such as evaporation or condensation. By identifying the precise position of the dividing surface in the interfacial region with a gauge degree of freedom, we exploit gauge-invariance requirements to consistently define the intensive variables for the interface. The model is verified under stringent conditions by employing high-precision nonequilibrium molecular dynamics simulations of a coexisting vapor-liquid Lennard-Jones fluid. We conclude that the interfacial temperature is determined using the surface tension as a ``thermometer,'' and can be significantly different from the temperatures of the adjacent phases.