A second order Langevin sampler preserving positive volume for isothermal isobaric ensemble

TL;DR

This paper introduces a second-order Langevin sampler for the NPT ensemble that ensures positive volume preservation, improves theoretical understanding, and offers a practical numerical scheme for molecular simulations.

Contribution

It develops a new second-order Langevin method for the NPT ensemble that guarantees positive volume and provides a rigorous theoretical foundation.

Findings

The new equations preserve the desired ensemble measure.

The proposed scheme guarantees positive volume during simulations.

Numerical experiments demonstrate the method's effectiveness.

Abstract

We propose in this work a second-order Langevin sampler for the isothermal-isobaric ensemble (the NPT ensemble), preserving a positive volume for the simulation box. We first derive the suitable equations of motion for particles to be coupled with the overdamped Langevin equation of volume by sending the artificial mass of the periodic box to zero in the work of Liang et. al. [J. Chem. Phys. 157(14)]. We prove the well-posedness of the new system of equations and show that its invariant measure is the desired ensemble. The new continuous time equations not only justify the previous cell-rescaling methods, but also allow us to choose a suitable friction coefficient so that one has additive noise after a change of variable by taking logarithm of the volume. This observation allows us to propose a second order weak scheme that guarantees the positivity of the volume. Various numerical experiments have been performed to demonstrate the efficacy of our method.