Dynamical Non-Equilibrium Molecular Dynamics

In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD), which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, implemented in the nineteen-seventies by Ciccotti, Jacucci and MacDonald, the approach permits one to separate the problem of dynamical evolution from the problem of sampling the initial condition. D-NEMD provides the theoretical framework to compute time-dependent macroscopic dynamical behaviors by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions generated from a suitable (equilibrium or non-equilibrium) distribution at time zero. We also discuss how to generate a large class of initial distributions. The same approach applies also to the calculation of the rate constants of activated processes. The range of problems treatable by this method is illustrated by discussing applications to a few key hydrodynamic processes (the “classical” flow under shear, the formation of convective cells and the relaxation of an interface between two immiscible liquids).