Computing the local pressure in molecular dynamics simulations

TL;DR

This paper derives and compares two equivalent methods for calculating local pressure in molecular dynamics simulations, demonstrating their accuracy even in small regions, which is crucial for inhomogeneous soft matter systems.

Contribution

It provides a simple derivation of two equivalent local pressure expressions based on the virial relation, clarifying their use in molecular dynamics simulations.

Findings

Both pressure expressions yield accurate results in small regions.

The derivation confirms the equivalence of boundary-based and interaction-based methods.

Simulations of osmotic systems validate the methods' effectiveness.

Abstract

Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic) pressure in a molecular dynamics simulation. One of these expressions, previously derived by other authors via a different route, involves summation over interactions between particles within the region of interest; the other involves summation over interactions across the boundary of the region of interest. We illustrate our derivation using simulations of a simple osmotic system; both expressions produce accurate results even when the region of interest over which the pressure is measured is very small.