A hydrodynamic theory for fluctuations around equilibrium of a liquid-vapour interface

We formulate a scheme describing the fluctuations of a liquid-vapour interface. This is done using a thermodynamic description of the system with singular densities and currents at the dividing surface. Equilibrium (equal time) correlation functions for e.g. the interfacial temperature and the location of the dividing surface are given. Landau-Lifshitz equations are formulated for the interfacial densities. These equations, as well as the boundary conditions, contain random contributions to the currents which are Gaussian and white. Fluctuations-dissipation theorems for these random currents are given.