Stochastic boundary conditions for molecular dynamics simulations

TL;DR

This paper introduces a stochastic boundary conditions method for molecular dynamics that enables grand canonical ensemble measurements by simulating particle injection and ejection based on collected statistics, improving finite system simulations.

Contribution

The paper presents a novel SBC approach that replaces periodic boundaries with stochastic particle injection/ejection, allowing grand canonical ensemble analysis in finite molecular dynamics simulations.

Findings

Successfully measured thermodynamic quantities like pair distribution function, compressibility, and specific heat.

Validated the SBC method against literature values for a hard disk gas.

Demonstrated the effectiveness of SBC in finite volume simulations.

Abstract

In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of injection/ejection events in periodic boundary conditions (PBC). Once sufficient statistics are collected, we remove the PBC and turn on the SBC. In the SBC simulations, we allow particles leaving the system to be truly ejected from the simulation, and randomly inject particles at the boundaries by resampling from the injection/ejection statistics collected from the current or previous simulations. With the SBC, we can measure thermodynamic quantities within the grand canonical ensemble, based on the particle number and energy fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a hard disk gas and measured the pair distribution function, the compressibility and the specific heat, comparing them against literature values.