When will a glass break? Not on the first stress cycle, usually. Not on the thousandth, often. But somewhere in between, accumulated damage reaches a threshold and the material fails. The exact cycle number varies — run the same experiment twice and you get different answers. This variability looks like noise. It isn't.
Maity, Khandare, Bhaumik, Sollich, and Sastry (arXiv:2602.21807) show that the scatter in fatigue failure times obeys a remarkably clean law. Take the logarithm of the failure time. Measure its standard deviation across many samples. That standard deviation is proportional to the mean log-failure-time, with a proportionality constant that decreases with system size.
This means two things. First, the variability is multiplicative, not additive. The noise doesn't add a random number of cycles to the failure time — it multiplies the failure time by a random factor. Logarithmic scaling transforms multiplicative processes into additive ones, which is why the law shows up in log-space. Each stress cycle doesn't add a fixed increment of damage; it multiplies the accumulated damage by a factor drawn from a distribution. The product of many such factors is a log-normal, and log-normals have the property that their log-standard-deviation scales with their log-mean.
Second, the law comes from the failure mechanism itself, not from sample preparation. Different samples of the same glass have different initial defect distributions — different “disorder.” You might expect this disorder to dominate the variability. It doesn't. The authors show through simulations and a stochastic damage accumulation model that even identical samples would show the same scaling, because the randomness is in how damage accumulates cycle by cycle, not in where it starts.
As the system gets larger, the distribution sharpens — the proportionality constant decreases. In the thermodynamic limit, failure times become deterministic. But real materials are finite, and for real glasses under real cyclic loading, the scatter is a feature of the physics, not an artifact of the measurement.
There's an elegance in finding a scaling law inside what looks like irreducible randomness. The failure times aren't predictable, but the distribution of failure times is. You can't say when a specific glass will break, but you can say exactly how much the answer will vary. The scatter is clean.
Based on S. Maity, P. Khandare, H. Bhaumik, P. Sollich, and S. Sastry, "Stochasticity of fatigue failure times in sheared glasses" (arXiv:2602.21807, February 2026).