A two-time-scale, two-temperature scenario for nonlinear rheology

We investigate a general scenario for ''glassy" or "jammed" systems driven by an external, nonconservative force, analogous to a sheer force in a flui d. In this scenario, the drive results in the suppression of the usual agin g process, and the correlation and response functions become time translati on invariant. The relaxation time and the response functions are then depen dent on the intensity of the drive and on temperature. We investigate this dependence within the framework of a dynamical closure approximation that b ecomes exact for disordered, fully connected models. The relaxation time is shown to be a decreasing function of the drive ("shear thinning" effect). The correlation functions below the glass transition temperature (T-c) disp lay a two-time-scale relaxation pattern, similar to that observed at equili brium slightly above T-c. We also study the violation of the fluctuation-di ssipation relationship in the driven system. This violation is very reminis cent of the one that takes place in a system aging below T-c at zero drive. It involves, in particular the appearance of a two-temperature regime, in the sense of an effective fluctuation-dissipation temperature [L. F. Cuglia ndolo, J. Kurchan, and L. Peliti, Phys. Rev. E 55, 3898 (1997)]. Although o ur results are, in principle, limited to the closure relations that hold fo r mean-field models, we argue that a number of the salient features are not inherent to the approximation scheme, and may be tested in experiments and simulations.