  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.
