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

Matthias Sachs (1) , Benedict Leimkuhler (2) , Vincent Danos (3, 4, 5)

1 Duke University [Durham]
2 School of Mathematics - University of Edinburgh
3 ANTIQUE - Analyse Statique par Interprétation Abstraite
4 CNRS - Centre National de la Recherche Scientifique
5 DI-ENS - Département d'informatique - ENS Paris

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.

Mots clés: Local thermal equilibrium; Sampling; Temperature gradients; Langevin dynamics; Fluctuation-dissipation theorems; Nonequilibrium simulation; Molecular dynamics

Domaines: Mathématiques [math]

Matthias Sachs, Benedict Leimkuhler, Vincent Danos. Langevin Dynamics with Variable Coefficients and Nonconservative Forces: From Stationary States to Numerical Methods. Entropy, 2017, 19 (12), pp.647. ⟨10.3390/e19120647⟩. ⟨hal-01976381⟩