The nonequilibrium statistical mechanics of Markov interacting particles

What the math gives to ML

The paper’s transferable mechanism is a path-space, rather than instantaneous, notion of conditional independence: exterior and interior histories factorise only when the boundary history screens all temporal and latent channels. This factorisation is equivalent to additive separation of conditional path log-likelihoods, while its violation is measured by conditional mutual information. For continuous-time neural dynamics, Girsanov’s theorem converts a drift change into stochastic-control energy, whose expectation equals relative entropy between path laws. These constructions support implementable regularizers for recurrent, state-space, world-model, and neural SDE architectures with quantitative diagnostics.