Geometric integrator for simulations in the canonical ensemble

TL;DR

This paper introduces a geometric integrator for molecular dynamics in the canonical ensemble that preserves invariant distributions, enabling consistent comparisons of thermostat effects on system dynamics.

Contribution

A unified, geometric integrator for density dynamics algorithms that maintains invariant distributions across various thermostats in molecular simulations.

Findings

Good conservation of geometrical properties in simulations.

Accurate thermodynamic results across thermostats.

Versatile application to Lennard-Jones systems.

Abstract

In this work we introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble. In particular, we consider the equations arising from the so-called density dynamics algorithm with any possible type of thermostat and provide an integrator that preserves the invariant distribution. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of the system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results.