  We address the system-size dependence of typical plastic flow events when an
amorphous solid is put under a fixed external strain rate at a finite
temperature. For system sizes that are accessible to numerical simulations at
reasonable strain rates and at low temperatures the magnitude of plastic events
grows with the system size. We explain however that this must be a finite size
effect; for larger systems there exist two cross-over length-scales $\xi_1$ and
$\xi_2$, the first determined by the elastic time-scale and the second by the
thermal energy-scale. For system of linear size $L$ larger than any of these
scales the magnitude of plastic events must be bounded. For systems of size
$L\gg \xi$ there must exist $(L/\xi)^d$ uncorrelated plastic events which occur
simultaneously. We present a scaling theory that culminates with the dependence
of the cross-over scales on temperature and strain rate. Finally we relate
these findings to the temperature and size dependence of the stress
fluctuations. We comment on the importance of these considerations for theories
of elasto-plasticity.
