Erratum: Nonequilibrium Shear Viscosity Computations with Langevin Dynamics

Joubaud, Rémi; Stoltz, Gabriel

doi:10.1137/12090040x

Cited by 1 publication

(2 citation statements)

References 5 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of Lemma 2.1 follows the same lines as the proof of uniform hypocoercive estimates in the corrected version of Theorem 3 in Joubaud & Stoltz (2012a) (see the erratum Joubaud & Stoltz (2013) or the updated preprint version Joubaud & Stoltz (2012b)). We provide a simplified version of it for completeness.…”

Section: Proofs Of the Resultsmentioning

confidence: 96%

See 1 more Smart Citation

The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics

Leimkuhler¹,

Matthews²,

2015

Self Cite

View full text Add to dashboard Cite

We consider numerical methods for thermodynamic sampling, i.e. computing sequences of points distributed according to the Gibbs-Boltzmann distribution, using Langevin dynamics and overdamped Langevin dynamics (Brownian dynamics). A wide variety of numerical methods for Langevin dynamics may be constructed based on splitting the stochastic differential equations into various component parts, each of which may be propagated exactly in the sense of distributions. Each such method may be viewed as generating samples according to an associated invariant measure that differs from the exact canonical invariant measure by a stepsize-dependent perturbation. We provide error estimatesà la Talay-Tubaro on the invariant distribution for small stepsize, and compare the sampling bias obtained for various choices of splitting method. We further investigate the overdamped limit and apply the methods in the context of driven systems where the goal is sampling with respect to a nonequilibrium steady state. Our analyses are illustrated by numerical experiments.

show abstract

Section: Proofs Of the Resultsmentioning

confidence: 96%

“…Recall that, unless otherwise mentioned, all operators are defined on S , and that formal adjoint operators are by default considered on L 2 (µ). Recall also that Joubaud & Stoltz (2013) or the updated preprint version Joubaud & Stoltz (2012b)). We provide a simplified version of it for completeness.…”

Section: Proofs Of the Resultsmentioning

confidence: 99%