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Entropy 2017, 19(12), 647; https://doi.org/10.3390/e19120647

Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods

1
Department of Mathematics, Duke University, Durham, NC 27708, USA
2
The School of Mathematics and the Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, University of Edinburgh, Edinburgh EH9 3FD, UK
3
Département d’informatique, École Normale Supérieure, 45 rue d’Ulm, F-75230 Paris CEDEX 05, France
*
Author to whom correspondence should be addressed.
Received: 27 September 2017 / Revised: 20 November 2017 / Accepted: 22 November 2017 / Published: 29 November 2017
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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Abstract

Langevin dynamics is a versatile stochastic model used in biology, chemistry, engineering, physics and computer science. Traditionally, in thermal equilibrium, one assumes (i) the forces are given as the gradient of a potential and (ii) a fluctuation-dissipation relation holds between stochastic and dissipative forces; these assumptions ensure that the system samples a prescribed invariant Gibbs-Boltzmann distribution for a specified target temperature. In this article, we relax these assumptions, incorporating variable friction and temperature parameters and allowing nonconservative force fields, for which the form of the stationary state is typically not known a priori. We examine theoretical issues such as stability of the steady state and ergodic properties, as well as practical aspects such as the design of numerical methods for stochastic particle models. Applications to nonequilibrium systems with thermal gradients and active particles are discussed. View Full-Text
Keywords: Langevin dynamics; fluctuation-dissipation theorems; nonequilibrium simulation; molecular dynamics; sampling; local thermal equilibrium; temperature gradients Langevin dynamics; fluctuation-dissipation theorems; nonequilibrium simulation; molecular dynamics; sampling; local thermal equilibrium; temperature gradients
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Sachs, M.; Leimkuhler, B.; Danos, V. Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods. Entropy 2017, 19, 647.

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