Non-Gaussian distribution of displacements for Lennard-Jones particles in equilibrium

TL;DR

This paper demonstrates that the common assumption of Gaussian distributions for particle displacements in meso-scale simulations is invalid over many scales, revealing the need for more complex models.

Contribution

It uncovers the non-Gaussian nature of particle displacements in Lennard-Jones systems across various coarse-graining scales, challenging standard assumptions.

Findings

Gaussian assumption fails at many scales

Displacements require complex distribution models

Impacts meso-scale simulation accuracy

Abstract

Most meso-scale simulation methods assume Gaussian distributions of velocity-like quantities. These quantities are not true velocities, however, but rather time-averaged velocities or displacements of particles. We show that there is a large range of coarse-graining scales where the assumption of a Gaussian distribution of these displacements fails, and a more complex distribution is required to adequately express these distribution functions of displacements.