Two-time scales, two-temperature scenario for nonlinear rheology

TL;DR

This paper explores how external driving forces affect the relaxation dynamics and fluctuation-dissipation relations in glassy and jammed systems, revealing a two-temperature regime and shear thinning effects.

Contribution

It introduces a theoretical framework for understanding driven glassy systems, highlighting the emergence of two-time scales and effective temperatures under non-conservative forces.

Findings

Relaxation time decreases with increasing drive (shear thinning).

Correlation functions exhibit two-time scale relaxation below Tc.

Violation of fluctuation-dissipation theorem indicates a two-temperature regime.

Abstract

We investigate a general scenario for ``glassy'' or ``jammed'' systems driven by an external, non-conservative force, analogous to a shear force in a fluid. In this scenario, the drive results in the suppression of the usual aging process, and the correlation and response functions become time translation invariant. The relaxation time and the response functions are then dependent on the intensity of the drive and on temperature. We investigate this dependence within the framework of a dynamical closure approximation that becomes 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 (Tc) display a two time scales relaxation pattern, similar to that observed at equilibrium slightly above Tc. We also study the violation of the fluctuation dissipation relationship in the driven system. This violation is very reminiscent of the one that takes place in a system aging below Tc at zero drive. It involves in particular the appearance of a two-temperatures regime, in the sense of an effective fluctuation dissipation temperature. Although our results are in principle limited to the closure relations that hold for 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.