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We consider the dynamics of the disordered trap model, which is known to becompletely out-of-equilibrium and to present strong localization effects in itsaging phase. We are interested into the influence of an external force, when itis applied from the very beginning at $t=0$, or only after a waiting time$t_w$. We obtain a "non-linear Fluctuation Theorem" for the correspondingone-time and two-time diffusion fronts in any given sample, that implies thefollowing consequences : (i) for fixed times, there exists a linear responseregime, where the Fluctuation-Dissipation Relation or Einstein relation isvalid even in the aging time sector, in contrast with other aging disorderedsystems; (ii) for a fixed waiting time and fixed external field, the validityof the linear response regime is limited in time by a characteristic timedepending on the external force; (iii) in the non-linear response regime, thereexists a very simple relation for the asymmetry in the position for theone-time and the two-times disorder averaged diffusion fronts in the presenceof an external force, in contrast to other models of random walks in randommedia. The present non-linear Fluctuation Theorem is a consequence of a specialdynamical symmetry of the trap model.Comment: 9 pages, no figur

On a non-linear fluctuation theorem for the ageing dynamics of disordered trap models