Bounds for Apparent Second-Law Violations in Quantum Trajectories

What the math gives to ML

The paper provides a sharp, distribution-free way to quantify apparent reversals in trajectory distributions using log-likelihood ratios rather than arbitrary scalar observables. Its transferable asset is the separation between a physical trajectory statistic sigma and a completion term sigma* together with an explicit lower bound on the probability of negative physical events from the mean completed asymmetry. This can be adapted to stochastic generative models, especially diffusion or learned Markov samplers, where forward and time-reversed path likelihoods are available. The most direct experiment is a fluctuation-consistency regularizer that prevents a learned sampler from hiding directional errors in rare, high-magnitude reverse trajectories.