Minimal-DKL models consistent with measured correlations

Construct models that, while matching empirically measured correlation functions of observed time-series, minimize the Kullback–Leibler divergence between the distribution of forward trajectories and their time-reversed counterparts, in order to improve direct, model-free estimates of irreversibility from data using analytic bounds.

Background

The paper introduces a model-free approach to estimate the arrow of time by directly computing the Kullback–Leibler divergence between distributions of observed trajectories and their time reversals, while correcting the bias due to finite sample sizes via extrapolation in the number of samples.

In the concluding discussion, the authors point to the potential of leveraging analytic bounds to further refine direct estimates of D_KL, drawing an analogy to maximum entropy methods. They suggest a concrete direction: constructing models that reproduce measured correlation functions yet minimize D_KL, which could provide principled lower-bound estimators or improved direct inference tools for irreversibility in partially observed, non-equilibrium systems.