Abstract
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).
Highlights
The most widespread use of Molecular Dynamics (MD) [1,2], in the same spirit of MonteCarlo (MC) [3,4], is to compute the thermodynamic or statistical behavior of molecular systems at Entropy 2014, 16 equilibrium
As a more advanced illustration of Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD) when sampling from a conditional probability density, we describe the case of the hydrodynamic relaxation to equilibrium of the interface between two immiscible liquids [61]
We have presented a dynamical approach to non-equilibrium MD, which makes it possible to compute, numerically, but, otherwise, rigorously, time-dependent non-equilibrium responses, i.e., to observe directly transient responses in non-stationary regimes
Summary
The most widespread use of Molecular Dynamics (MD) [1,2], in the same spirit of Monte. In the case of Kubo’s procedure one does not need to make reference to an initial equilibrium state, but can, rather, refer to an arbitrary initial distribution at time t0 = 0 of the system This result has an important consequence for Molecular Dynamics simulations, since it allows one to separate the problem of dynamical evolution from the problem of sampling the initial condition. Starting from the mid-nineteen-seventies, the direct numerical simulation of the response was used in conjunction with a sample of initial conditions extracted from an equilibrium trajectory [10,11] In this context, the problem of achieving a reasonable signal-to-noise ratio, even for weak perturbations, was solved for short times by introducing the so-called subtraction technique [12], which permitted one to verify, with surprising results [13], the range of the validity of linearity.
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