Hyperuniform systems are maximally irreversible

What the math gives to ML

The paper supplies a path-integral view of stochastic dynamics in which the log ratio between a trajectory and its time reversal is an explicit entropy-production functional. This can be transferred to neural-network training as a quantitative measure of how far optimizer dynamics depart from reversible behavior, rather than treating irreversibility only as an informal property of SGD. The most practical use is an online diagnostic and controller for optimizer noise, learning rate, or momentum: unusually large forward/reverse path-log ratios should identify unstable or wasteful training phases. A stronger experimental variant can add a bounded penalty on trajectory irreversibility and test whether it improves stability at equal optimization progress.