Amorphous solids — glasses, metallic alloys, dense colloids — deform through discrete rearrangements. A local region yields, redistributes stress to its neighbors, and some of those neighbors yield in turn. The resulting avalanche follows power-law statistics: many small events, few large ones, no characteristic scale. This is the intermittent regime, and it is well-studied under external mechanical driving.
Rodriguez-Lopez and Ferrero show that thermal activation alone, without any external stress, can push the system out of this regime entirely. At low temperatures, the avalanche statistics look like the driven case: scale-free with an exponential cutoff that grows with system size. But above a critical temperature T_c(L), a qualitative change occurs. System-spanning runaway events appear — avalanches that temporarily fluidize the entire material. The intermittent regime is replaced by something more violent.
The finite-size scaling is where the physics gets interesting. The critical temperature decreases algebraically with system size: T_c(L) ~ L^(-alpha). This means that as the system grows, the temperature needed to trigger runaway avalanches drops. In the thermodynamic limit — an infinite system — any nonzero temperature would be above critical. The intermittent regime, which is the normal state of glasses at room temperature, would be unstable to arbitrarily weak thermal fluctuations.
Real glasses are finite, so the runaway regime requires finite temperature. But the scaling tells us that larger samples of amorphous material are closer to instability than smaller ones. A micron-scale metallic glass sits comfortably in the intermittent regime at room temperature. A meter-scale sample of the same material is closer to the edge. The physics is the same; the system size controls the distance to the transition.
The mechanism is reorganization of marginal stability. Thermal fluctuations don't just trigger individual yielding events — they reshape the distribution of distances to yielding across the entire material. At low temperature, this redistribution is too slow to create system-spanning correlations. At high temperature, the redistribution outruns the relaxation, and local yielding events cascade before stability can be re-established. The glass briefly becomes a liquid, then freezes again.
This is different from the glass transition itself, which is an equilibrium (or near-equilibrium) phenomenon. The runaway avalanches are far-from-equilibrium events driven by the interplay between thermal activation and elastic stress redistribution. The glass is solid before and after. What happens in between is a collective failure that the material recovers from — not melting, but fluidization.