Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems

Abstract

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently-developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

15 pages, 2 figures, and 2 tables

References in corpus (3)

• Accurate sampling using Langevin dynamics
• Isothermal-isobaric molecular dynamics using stochastic velocity rescaling
• Path sampling with Stochastic Dynamics: Some new Algorithms

Cited by in corpus (26)

• Theory of nonequilibrium free energy transduction by molecular machines
• Autonomous artificial intelligence discovers mechanisms of molecular self-organization in virtual experiments
• Escape dynamics of active particles in multistable potentials
• Complete Set of Stochastic Verlet-Type Thermostats for Correct Langevin Simulations
• On the effect of the thermostat in non-equilibrium molecular dynamics simulations
• Ensuring thermodynamic consistency with invertible coarse-graining
• Dissipation bounds the amplification of transition rates far from equilibrium
• Non-equilibrium steady state of a driven levitated particle with feedback cooling
• Preserving Correlations Between Trajectories for Efficient Path Sampling
• Non-Adiabatic Vibrational Damping of Molecular Adsorbates: Insights into Electronic Friction and the Role of Electronic Coherence
• Nonequilibrium dynamics induced by scattering forces for optically trapped nanoparticles in strongly inertial regimes
• Giant diffusion of nanomechanical rotors in a tilted washboard potential
• Path probability ratios for Langevin dynamics -- exact and approximate
• The role of non-conservative scattering forces and damping on Brownian particles in optical traps
• Limits on the Precision of Catenane Molecular Motors: Insights from Thermodynamics and Molecular Dynamics Simulations
• Static and Dynamic Properties of Block-Copolymer Based Grafted Nanoparticles Across the Non-Ergodicity Transition
• Static and Dynamic Properties of Block-Copolymer Based Grafted Nanoparticles Across the Non-Ergodicity Transition
• The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics
• Generalized Moment Correction for Long-Ranged Electrostatics
• Bringing discrete-time Langevin splitting methods into agreement with thermodynamics
• Path-accelerated molecular dynamics: Parallel-in-time integration using path integrals
• White-noise fluctuation theorem for Langevin dynamics
• On the Definition of Velocity in Discrete-Time, Stochastic Langevin Simulations
• Mass-Zero constrained molecular dynamics for electrostatic interactions
• GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms
• Linear Analysis of Stochastic Verlet-Type Integrators for Langevin Equations