Generalized Einstein Relation

The connection between diffusion coefficient and mobility, known as the Einstein relation is fundamental in equilibrium statistical physics. The Einstein relation, however, breaks down when the system is sufficiently out of equilibrium where linear response theories are not applicable. To study the violation we create a non-equilibrium steady state (NESS) using scanning optical laser tweezers whose intensity is modulated along the scanning direction. We analyze the particles motion as a function of the driving force and observe that the classical Einstein relation is violated. In order to restore a relation between the diffusion coefficient and the mobility, one has to additionally consider a violation function which is also experimentally accessible. We demonstrate that this generalized Einstein relation is indeed observed in our experiments.