Advanced Langevin thermostats: Properties, extensions to rheology, and a lean momentum-conserving approach

TL;DR

This paper reviews and extends Langevin thermostats, demonstrating their advantages over traditional methods, and introduces new variants including a colored and a momentum-conserving thermostat for improved simulation accuracy.

Contribution

It combines and extends existing Langevin thermostats, providing new derivations and proposing innovative extensions such as a colored and a lean momentum-conserving thermostat.

Findings

Langevin thermostats outperform global kinetic-energy controls.

The Gr{ }nbech-Jensen scheme offers high accuracy.

New thermostats improve simulation fidelity and conservation properties.

Abstract

The Langevin equation accounts for unresolved bath degrees of freedom driving the system toward the bath temperature. Because of this, numerical solutions of the Langevin equation have a long history. Here, we recapitulate, combine, and extend existing Langevin-equation based thermostats, scrutinize their properties and demonstrate their superiority over global kinetic-energy controls. Our work includes compact, asymptotic-analysis based derivations of stochastic thermostats, including the highly accurate Gr{\o}nbech-Jensen scheme. Proposed extensions include a precise, colored and a lean, momentum-conserving thermostat.