Effects of an external drive on the fluctuation - dissipation relation of phase - ordering systems

– The relation between the autocorrelation C(t, tw) and the integrated linear response function χ(t, tw) is studied in the context of the large-N model for phase-ordering systems subjected to a shear flow. In the high temperature phase T > Tc a non-equilibrium stationary state is entered which is characterized by a non-trivial fluctuation-dissipation relation χ(t − tw) = ˜ χ(C(t − tw)). For quenches below Tc the splitting of the order parameter field into two statistically independent components, responsible for the stationary C st (t − tw) and aging C ag (t/tw) part of the autocorrelation function, can be explicitly exhibited in close analogy with the undriven case. In the regime t − tw ≪ tw the same relation χ(t − tw) = ˜ χ(C st (t − tw)) is found between the response and C st (t − tw), as for T > Tc. The aging part of χ(t, tw) is negligible for tw → ∞, as without drive, resulting in a flat χ(C) in the aging regime t − tw ≫ tw. Understanding non-equilibrium processes is a central topic of modern statistical physics. Many systems in nature are observed in a persistent non-equilibrium regime. Among these two important categories can be identified according to the asymptotic state towards which they evolve. Systems subjected to a change of thermodynamic variables, such as temperature or pressure, belong to the first class. In this case, an equilibrium state is approached which, however, can be hardly reached if the ergodic time grows in the thermodynamic limit. This is usually observed when the initial and final states are separated by a phase transition. Typical examples are glassy materials or phase-separating systems quenched below the critical temperature. The off-equilibrium dynamics in this case is characterized by the aging property of the autocorrelation function [1]. A different situation, on the other hand, is observed when external power is injected into a system with rate γ by doing work on it, as in the case of stirred or sheared materials. In this case a time translational invariant (TTI) stationary regime can be entered, depending on the thermodynamic parameters, which is not an equilibrium state.