# The virial theorem with periodic boundary conditions

## TL;DR

This paper reformulates the virial theorem to be applicable to both confined and periodic systems, enabling more accurate analysis of stresses in molecular simulations.

## Contribution

The authors present a modified virial theorem that is valid for periodic boundary conditions, bridging a gap in existing formulations.

## Key findings

- Validated the new formulation with Monte Carlo and molecular dynamics simulations
- Demonstrated the theorem's applicability to small systems with periodic boundaries
- Provided a consistent way to relate boundary stresses to interior forces

## Abstract

The virial theorem relates averages of kinetic energy and forces in confined systems. It is widely used to relate stresses in molecular simulation as measured at a boundary and in the interior of a system. In periodic systems, the theorem must be modified in order to produce useful results. We formulate the theorem so that it is valid for both confined and for periodic systems. We cross-check our formulation in a study of a small system using both Monte Carlo and molecular dynamics simulations.