  Developing a macroscopic theory of elasto-plasticity in amorphous solids
calls for (i) identifying the relevant macro state-variables and (ii)
discriminating the different time-scales which characterize these variables. In
current theories it is assumed that the stress reaches its elasto-plastic
steady state value on the same time-scale as the configurational variables (be
they the configurational energy, configurational entropy or the effective
temperature). By examining numerical simulations in two and three dimensions we
show that this is generally not the case, the configurational degrees of
freedom may reach the elasto-plastic steady state on the time scales which can
be very different from the time scale of the stress. We provide a physical
discussion to rationalize these findings.
