TimeArrowMob: A Controlled Benchmark for Temporal Directionality and Irreversibility in Human Mobility and Beyond

Real-world human mobility trajectories provide rich and realistic temporal structure, but their true temporal directionality and time irreversibility are unknown, leaving existing methods without reliable ground truth for evaluation. Conversely, trajectories generated from hand-crafted rules or a single physical model can provide controlled directionality but may differ substantially from complex human mobility. We introduce TimeArrowMob, a controlled benchmark that combines real mobility structure with analytically computable temporal-direction ground truth. Taking each YJMob100K user trajectory as an independent unit, we construct a reversible baseline from its locations and symmetrized transition counts. We then impose controllable circulation constraints on transition counts and generate closed trajectories through Eulerian circuits, matching trajectory length, location frequencies, undirected transition counts, and self-transition counts across directions and strength levels. The construction generates paired Forward/Reverse trajectories with exact direction labels and additive local log-likelihood-ratio contributions relative to a fixed reference mechanism, while reversal-symmetric sampling provides zero-direction controls. The strength of the temporal arrow is explicitly controlled through the circulation scale and computed as the normalized magnitude of the summed reference contributions. Grounded in time-reversal symmetry and probabilistic inference, TimeArrowMob provides realistic trajectory morphology together with exact supervision for direction, strength, and localization. The framework enables systematic evaluation of irreversibility estimators, learning-based direction predictors, and attribution methods, and can be extended to other time-series domains with domain-valid reversal units.