PIMS - CSC Seminar: David Sivak

Stochastic differential equations of motion (e.g., the Langevin equation) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. I will show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. This framework permits the quantification, for the first time, of the deviations from the desired equilibrium distribution in Langevin simulations of solvated systems. I will show that incorporating a novel time step rescaling corrects a number of dynamical defects in these integrators, and moreover that one particular discrete splitting of the equations of motion possesses essentially universally appropriate properties for Langevin simulations of molecular systems in equilibrium, nonequilibrium, and path sampling contexts.