Spatiotemporal hierarchy of slow avalanches during creep.

Far from equilibrium, amorphous solids exhibit structural relaxations that span a vast range of timescales such as physical aging and creep. Recently, it has been shown that such relaxations are driven by intermittent, scale-free, yet anomalously slow sequences of local rearrangements, termed "thermal avalanches." Here, we investigate the spatio-temporal dynamics of these avalanches during logarithmic creep using simulations of a mesoscale model of amorphous solids. By systematically disentangling mechanical and thermal activation events, we reveal that thermal avalanches have a hierarchical spatio-temporal structure: localized rearrangement events group into fast and compact cascades, which then promote the thermal activation of subsequent cascades via long-range, noise-mediated facilitation. This process results in heavy-tailed temporal correlations reminiscent of seismic activity. We validate these findings using experiments on slow relaxation of crumpled matter. Our work provides a framework for identifying noise-mediated correlations and elucidates the rich structural dynamics underlying slow relaxation of amorphous solids.