Convergence of Nonequilibrium Langevin Dynamics for Planar Flows

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) such as Lees–Edwards PBCs and Kraynik–Reinelt PBCs to treat respectively shear flow and planar elongational flow. The convergence is shown using a technique similar to (Joubaud et al. in J Stat Phys 158:1–36, 2015).