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.
| Original language | English |
|---|---|
| Article number | 647 |
| Journal | Entropy |
| Volume | 19 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Dec 2017 |
Bibliographical note
Funding Information:Acknowledgments: The research of all three authors was supported by the ERC project RULE (grant number 320823). The collaboration was initiated during a residency of the first two authors at the Institut Henri Poincaré and its program on “Stochastic dynamics out of equilibrium.” The work of M. Sachs was further supported by the Statistical and Applied Mathematical Sciences Institute (North Carolina).
Publisher Copyright:
© 2017 by the authors.
Keywords
- Fluctuation-dissipation theorems
- Langevin dynamics
- Local thermal equilibrium
- Molecular dynamics
- Nonequilibrium simulation
- Sampling
- Temperature gradients
ASJC Scopus subject areas
- Information Systems
- Mathematical Physics
- Physics and Astronomy (miscellaneous)
- Electrical and Electronic Engineering