Time asymmetry of the Kramers equation with nonlinear friction: Fluctuation-dissipation relation and ratchet effect

We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by studying the generalized fluctuation-dissipation relation for this ratchet model driven by Coulomb friction.