Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/12/647 |
| _version_ | 1798002357908275200 |
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| author | Matthias Sachs Benedict Leimkuhler Vincent Danos |
| author_facet | Matthias Sachs Benedict Leimkuhler Vincent Danos |
| author_sort | Matthias Sachs |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:51:52Z |
| format | Article |
| id | doaj.art-449dcc122e8c4aae95ca68be51fa2252 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T11:51:52Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-449dcc122e8c4aae95ca68be51fa22522022-12-22T04:25:19ZengMDPI AGEntropy1099-43002017-11-01191264710.3390/e19120647e19120647Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical MethodsMatthias Sachs0Benedict Leimkuhler1Vincent Danos2Department of Mathematics, Duke University, Durham, NC 27708, USAThe School of Mathematics and the Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, University of Edinburgh, Edinburgh EH9 3FD, UKDépartement d’informatique, École Normale Supérieure, 45 rue d’Ulm, F-75230 Paris CEDEX 05, FranceLangevin 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.https://www.mdpi.com/1099-4300/19/12/647Langevin dynamicsfluctuation-dissipation theoremsnonequilibrium simulationmolecular dynamicssamplinglocal thermal equilibriumtemperature gradients |
| spellingShingle | Matthias Sachs Benedict Leimkuhler Vincent Danos Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods Entropy Langevin dynamics fluctuation-dissipation theorems nonequilibrium simulation molecular dynamics sampling local thermal equilibrium temperature gradients |
| title | Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods |
| title_full | Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods |
| title_fullStr | Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods |
| title_full_unstemmed | Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods |
| title_short | Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods |
| title_sort | langevin dynamics with variable coefficients and nonconservative forces from stationary states to numerical methods |
| topic | Langevin dynamics fluctuation-dissipation theorems nonequilibrium simulation molecular dynamics sampling local thermal equilibrium temperature gradients |
| url | https://www.mdpi.com/1099-4300/19/12/647 |
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