The Challenge of Stochastic St{\o}rmer-Verlet Thermostats Generating Correct Statistics
Joshua Finkelstein, Chungho Cheng, Giacomo Fiorin, Benjamin Seibold,, Niels Gr{\o}nbech-Jensen

TL;DR
This paper investigates stochastic Størmer-Verlet algorithms for Langevin equations, concluding that methods with multiple random variables per step are unnecessary and recommending the GJ-I/GJF-2GJ method for statistical accuracy due to minimal time-scaling.
Contribution
It proves that only identical random variables per step can produce correct statistics and identifies the GJ-I/GJF-2GJ method as optimal for statistical simulations.
Findings
Two random variables per step are equivalent to one for correct statistics.
The GJ-I/GJF-2GJ method has minimal inherent time-scaling.
Different methods exhibit varying stability linked to their time-scaling.
Abstract
In light of the recently developed complete GJ set of single random variable stochastic, discrete-time St{\o}rmer-Verlet algorithms for statistically accurate simulations of Langevin equations, we investigate two outstanding questions: 1) Are there any algorithmic or statistical benefits from including multiple random variables per time-step, and 2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational free-particle diffusion, and that these requirements only can be…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
