{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:25:33Z","timestamp":1772252733310,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,4,26]],"date-time":"2018-04-26T00:00:00Z","timestamp":1524700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003825","name":"Hungarian Academy of Science","doi-asserted-by":"publisher","award":["bilateral mobility grant"],"award-info":[{"award-number":["bilateral mobility grant"]}],"id":[{"id":"10.13039\/501100003825","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008725","name":"Polish Academy of Sciences","doi-asserted-by":"publisher","award":["bilateral mobility grant"],"award-info":[{"award-number":["bilateral mobility grant"]}],"id":[{"id":"10.13039\/501100008725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>While Langevin integrators are popular in the study of equilibrium properties of complex systems, it is challenging to estimate the timestep-induced discretization error: the degree to which the sampled phase-space or configuration-space probability density departs from the desired target density due to the use of a finite integration timestep. Sivak et al., introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the Kullback-Leibler (KL) divergence, in phase space, but did not specifically address the issue of configuration-space properties, which are much more commonly of interest in molecular simulations. Here, we introduce a variant of this near-equilibrium estimator capable of measuring the error in the configuration-space marginal density, validating it against a complex but exact nested Monte Carlo estimator to show that it reproduces the KL divergence with high fidelity. To illustrate its utility, we employ this new near-equilibrium estimator to assess a claim that a recently proposed Langevin integrator introduces extremely small configuration-space density errors up to the stability limit at no extra computational expense. Finally, we show how this approach to quantifying sampling bias can be applied to a wide variety of stochastic integrators by following a straightforward procedure to compute the appropriate shadow work, and describe how it can be extended to quantify the error in arbitrary marginal or conditional distributions of interest.<\/jats:p>","DOI":"10.3390\/e20050318","type":"journal-article","created":{"date-parts":[[2018,4,26]],"date-time":"2018-04-26T04:17:52Z","timestamp":1524716272000},"page":"318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3719-266X","authenticated-orcid":false,"given":"Josh","family":"Fass","sequence":"first","affiliation":[{"name":"Tri-Institutional PhD Program in Computational Biology &amp; Medicine, New York, NY 10065, USA"},{"name":"Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4815-4722","authenticated-orcid":false,"given":"David A.","family":"Sivak","sequence":"additional","affiliation":[{"name":"Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada"}]},{"given":"Gavin E.","family":"Crooks","sequence":"additional","affiliation":[{"name":"Rigetti Computing, Berkeley, CA 94710, USA"}]},{"given":"Kyle A.","family":"Beauchamp","sequence":"additional","affiliation":[{"name":"Counsyl, South San Francisco, CA 94080, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8504-7091","authenticated-orcid":false,"given":"Benedict","family":"Leimkuhler","sequence":"additional","affiliation":[{"name":"School of Mathematics and Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, Kings Buildings, University of Edinburgh, Edinburgh EH9 3FD, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0542-119X","authenticated-orcid":false,"given":"John D.","family":"Chodera","sequence":"additional","affiliation":[{"name":"Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1119\/1.18725","article-title":"Paul Langevin\u2019s 1908 paper \u201cOn the Theory of Brownian Motion\u201d [\u201cSur la th\u00e9orie du mouvement brownien,\u201d C. 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