Cugliandolo and Iguain Reply:

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

“…We have obtained the following consequences : (i) in the linear response regime, the Fluctuation-Dissipation Relation or Einstein relation (26) is valid even in the aging time sector; (ii) for a fixed waiting time t w and fixed external field f , the validity of the linear response regime is limited in the time (t − t w ) by the characteristic time t µ (f ) ∼ (βf ) The results (i) and (ii) are in full agreement with the scaling analysis and the numerical simulations presented in [33], and we hope that our approach in some sense "explains" why aging trap models, which are known to present strong localization effects and to be completely out-of-equilibrium (see for instance the effective dynamics described in [32]), nevertheless satisfies the Fluctuation-Dissipation Relation in the whole linear response regime, in contrast with many disordered systems which present a non-trivial violation in the linear response regime [5,6,7].…”

“…where the distribution of the energies E n presents the exponential tail (6) to mimic the lowest energies statistics found in the Random Energy Model [37] and the distribution of free energy of states in the replica theory of spin-glasses [38]. This choice is moreover reinforced [39] by the exponential tail of the Gumbel distribution which represents one universality classes of extreme-value statistics.…”

“…We now consider the following aging experiment [33], which is very usual in the study of disordered systems [5,6,7] : the system first evolves with no external force f = 0 during the interval [0, t w ], and then evolves in the presence of the external force (f ) for t ≥ t w . We consider the two-time diffusion front P (f ;tw) (n, t; n w , t w |0, 0) which represents the joint probability to be at position n w at time t w and at position n at time t (where it is assumed that t > t w ).…”

“…For instance, a system can be out-of-equilibrium because it is driven in a non-equilibrium steady state by external boundary conditions or driving forces [1,2,3] or because it remains forever non-stationary and presents aging, such as in coarsening dynamics [4] or in disordered models [5,6,7].…”

“…On the other hand, in the field of aging dynamics of disordered models, the proposed generalization of the Fluctuation-Dissipation Theorem concerns the linear response regime and consists in introducing a FluctuationDissipation ratio to describe the modified relation between the two-time response function and the two-time correlation [5,6,7]. The introduction of this FDT violation ratio for the linear response regime has been also very useful to characterize the coarsening dynamics in non-disodered systems [15,16,17].…”