A Second-Order Langevin Sampler Preserving Positive Volume for Isothermal–Isobaric Ensemble (Communications in Computational Physics, 2025)
We propose in this work a second-order Langevin sampler for theisothermal-isobaric ensemble (the NPT ensemble), preserving a positive volume forthe simulation box. We first derive the suitable equations of motion for particles tobe 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 thatits invariant measure is the desired ensemble. The new continuous time equations notonly justify the previous cell rescaling methods, but also allow us to choose a suitablefriction coefficient so that one has additive noise after a change of variable by takinglogarithm of the volume. This observation allows us to propose a second-order weakscheme that guarantees the positivity of the volume. Various numerical experimentshave been performed to demonstrate the efficacy of our method.