  We study the rheology of amorphous solids in the limit of negligible thermal
fluctuations. On the basis of general arguments, the flow curve is shown to
result from an interplay between the time scales of the macroscopic driving and
the (cascades of) local particle rearrangements. Such rearrangements are known
to induce a redistribution of the elastic stress in the system. Although
mechanical noise, i.e., the local stress fluctuations arising from this
redistribution, is widely believed to activate new particle rearrangements, we
provide evidence that casts severe doubt on the analogy with thermal
fluctuations: mechanical and thermal fluctuations lead to asymptotically
different statistics for barrier crossing. These ideas are illustrated and
supported by a simple coarse-grained model whose ingredients are directly
connected with the physical processes relevant for the flow.
