Hydrodynamics from statistical mechanics: combined dynamical-NEMD and conditional sampling to relax an interface between two immiscible liquids

We present a method to study hydrodynamic phenomena from atomistic simulations. In statistical mechanics, these fields are computed as the ensemble average over the time dependent probability density function corresponding to the time evolution of an initial conditional probability density function consistent with some initial conditions. These initial conditions typically consist in constraints on some macroscopic fields, e.g. the density field. We show how these processes can be studied by combining the dynamical approach to non-equilibrium molecular dynamics with the restrained simulation approach. As an illustration of our method, we study the relaxation to the equilibrium of an interface between two immiscible liquids. We show that, at a variance with the local time average method, the standard atomistic approach used in this field, our method is able to produce (macroscopic) fields satisfying the symmetry conditions of the problem.