Displacements, mean-squared displacements, and codisplacements for the calculation of nonequilibrium properties

We study two situations in which nonequilibrium phenomena can be efficiently calculated using displacements, mean-squared displacements, or codisplacements instead of accumulating velocities or currents. The flow velocity profile for a fluid confined within a pore can be expressed as a sum of displacements within slabs from a molecular dynamics trajectory. In this form, an accurate flow profile is obtained from very sparse sampling of the trajectory. We also recast the linear response theory expression for the flow velocity profile in terms of mean codisplacements and demonstrate that this provides an efficient route for estimating the Green-Kubo expression for the velocity profile. Finally, we calculate the ionic contribution to the frequency-dependent electric susceptibility using dipolar displacements, instead of the conventional current-current correlation function. We expect these methods to be useful for generating transport properties from stored trajectories in very large systems or systems where relaxation times are long.