Generalised Langevin equation of many-body systems coupled to nonequilibrium environment

Abstract: We set up a mesoscopic theory for interacting Brownian particles embedded in a nonequilibrium environment, starting from the microscopic interacting many-body theory. Using nonequilibrium linear-response theory, we characterize the effective dynamical interactions on the mesoscopic scale and the statistics of the nonequilibrium environmental noise, arising upon integrating out the fast degrees of freedom. We apply our general results to a prototypical model, namely, two colloids embedded in a driven particles bath, which allows to easily observe the breakdown of the fluctuation-dissipation and action-reaction relations, hallmarks of nonequilibrium.