Emergent Second Law for Time-Dependent Nonequilibrium States
arXiv:2608.21661
2026
Dynamics
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper derives a nonautonomous macroscopic second law: fluctuations around a time-dependent most-probable evolution are constrained by entropy production evaluated along the trajectory generated by the time-reversed driving protocol. Its transferable asset is a computable forward/reverse path-likelihood ratio for systems whose control parameters, energy landscape, or noise statistics change in time, together with the prediction that the resulting bound becomes tight to first order under slow driving and linear response. A neural-network optimizer can use this ratio as an online irreversibility monitor and regulate learning-rate, noise, or curriculum schedules before training enters an unstable high-dissipation regime.
Ideas from this paper
✗ Mechanism failed
2026
Treat stochastic optimization with a time-dependent learning-rate, momentum, weight-decay, or data-mixture schedule as a nonautonomous Markov process. Estimate the entropy production of each parameter trajectory by comparing its forward transition likelihood with the likelihood under a separately simulated optimizer driven by the reversed schedule, then use this estimate to adapt the learning rate or injected gradient noise. The controller is designed to remain in a low-dissipation regime…
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