Convergence of Nonequilibrium Langevin Dynamics for Planar Flows

TL;DR

This paper proves that two-dimensional nonequilibrium Langevin dynamics under shear and elongational flows converges exponentially to a steady-state limit cycle, using advanced boundary condition techniques and coordinate transformations.

Contribution

It establishes exponential convergence of NELD to a limit cycle in 2D flows, employing automorphism remapping and Lagrangian coordinates.

Findings

Exponential convergence to steady-state limit cycle.

Effective use of Lees-Edwards and Kraynik-Reinelt PBCs.

Application of coordinate transformation techniques.

Abstract

We prove that incompressible two dimensional nonequilibrium Langevin dynamics (NELD) converges exponentially fast to a steady-state limit cycle. We use automorphism remapping periodic boundary conditions (PBCs) techniques such as Lees-Edwards PBCs and Kraynik-Reinelt PBCs to treat respectively shear flow and planar elongational flow. After rewriting NELD in Lagrangian coordinates, the convergence is shown using a technique similar to [R. Joubaud, G. A. Pavliotis, and G. Stoltz,2014].