@article{1119b78e18d64d2684d3ee9cf5606976,
title = "Longtime convergence of the temperature-accelerated molecular dynamics method",
abstract = "The equations of the temperature-accelerated molecular dynamics (TAMD) method for the calculations of free energies and partition functions are analyzed. Specifically, the exponential convergence of the law of these stochastic processes is established, with a convergence rate close to the one of the limiting, effective dynamics at higher temperature obtained with infinite acceleration. It is also shown that the invariant measures of TAMD are close to a known reference measure, with an error that can be quantified precisely. Finally, a central limit theorem is proven, which allows the estimation of errors on properties calculated by ergodic time averages. These results not only demonstrate the usefulness and validity range of the TAMD equations, but they also permit in principle to adjust the parameter in these equations to optimize their efficiency.",
keywords = "Poisson equation, longtime convergence, molecular dynamics, stochastic differential equation",
author = "Gabriel Stoltz and Eric Vanden-Eijnden",
note = "Funding Information: Part of this work was done during the authors{\textquoteright} stay at the Institut Henri Poincar{\'e}—Centre Emile Borel during the trimester {\textquoteleft}Stochastic Dynamics Out of Equilibrium{\textquoteright} (April–July 2017). The authors warmly thank this institution for its hospitality, and Inria Paris who funded the stay of EVE through an invited professor fellowship. The work of GS was funded in part by the Agence Nationale de la Recherche, under grant ANR-14-CE23-0012 (COSMOS) and by the European Research Council under the European Union{\textquoteright}s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement number 614492. He also benefited from the scientific environment of the Laboratoire International Associ{\'e} between the Centre National de la Recherche Scientifique and the University of Illinois at Urbana-Champaign. The work of EVE was funded in part by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under award number DMR-1420073 and by NSF under award number DMS-1522767. Publisher Copyright: {\textcopyright} 2018 IOP Publishing Ltd & London Mathematical Society.",
year = "2018",
month = jul,
day = "4",
doi = "10.1088/1361-6544/aac541",
language = "English (US)",
volume = "31",
pages = "3748--3769",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "8",
}