  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].
