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The distinction between the damping coefficient and the effective non-linearmobility of driven particles in active micro-rheology of supercooled liquids isexplained in terms of individual and collective dynamics. The effectivemobility arises as a collective effect which gives insight into the energylandscape of the system. On the other hand, the damping coefficient is aconstant that modulates the effect of external forces over the thermal energywhich particles have at their disposition to perform Brownian motion. For longtimes, these thermal fluctuations become characterized in terms of an effectivetemperature that is a consequence of the dynamic coupling between kinetic andconfigurational degrees of freedom induced by the presence of the strongexternal force. The interplay between collective mobility and effectivetemperature allows to formulate a generalized Stokes-Einstein relation that maybe used to determine the collective diffusion coefficient. The explicitrelations we deduce reproduce simulation data remarkably well.

Origin of the effective mobility in non-linear active micro-rheology