Generalised Langevin equation for nonequilibrium systems

We derive a generalized Langevin Equation (GLE) for the evolution of an arbitrary phase variable in a classical fluid that is initially at equilibrium and is subsequently subjected to an external field and a thermostat of the type used in nonequilibrium molecular dynamics computer simulations. The nonequilibrium steady state GLE is shown to have the same form as the equilibrium GLE at long times. We use our generalized Langevin equation to derive a simple Langevin equation for the motion of a single heavy Brownian particle in a solvent under steady state planar shear