Formulation of Liouville's Theorem for Grand Ensemble Molecular Simulations

TL;DR

This paper explores the formulation of Liouville's theorem within grand ensemble molecular simulations, addressing a gap in the literature concerning open systems with variable particle numbers.

Contribution

It introduces the concept of Liouville's theorem for grand ensemble systems, a novel theoretical development for molecular simulation of open systems.

Findings

Highlights the lack of explicit Liouville's theorem for grand ensembles.

Proposes a potential formulation for open systems with changing particle numbers.

Stimulates discussion on fundamental principles of molecular simulation.

Abstract

Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this note is to stimulate a debate about this crucial issue for molecular simulation.