Local and instantaneous definition of liquid-vapor interface at the microscopic scale

A novel definition of liquid-vapor interface at the molecular level is proposed, which can capture the local and instantaneous fluctuation of the interface. This definition is not based on the time- and space-averaged density profile, but on the instantaneous particle density distribution of molecules. Previously, the Gibbs dividing surface, which is the mathematical difinition decided from static density profile, is used to analyze the structure or interfacial physics. However, in this physical picture of the interface, the fluctuation itself and structure embedded in the fluctuation cannot be extracted. In this paper, we discuss the relation between the Gibbsian interface defined thermodynamically and the statistical-averaged interface of the local and instantaneous interface presented here. Furthermore, the interfacial fluctuation is evaluated by using the local and instantaneous interface, and an asymptotic character of the fluctuation is compared with the fluctuation predicted by the macroscopic capillary wave theory.