Computing memory functions from molecular dynamics simulations

We propose a new method to compute reliable estimates for memory functions of dynamical variables from molecular dynamics simulations. The key point is that the dynamical variable under consideration, which we take to be the velocity of a fluid particle, is modeled as an autoregressive stochastic process. The parameters of this stochastic process can be determined from molecular dynamics trajectories using efficient algorithms that are well established in signal processing. The procedure is also referred to as the maximum entropy method. From the autoregressive model of the velocity autocorrelation function we compute the one-sided z transform of the discretized memory function and the memory function itself. Using liquid argon as a simple model system, we demonstrate that the autocorrelation function and its power spectrum can be approximated to almost arbitrary precision. The same is therefore true for the memory function, which is calculated within the same stochastic model.