Emergent Detailed Balance in Human Mobility under Temporal Coarse-Graining

TL;DR

This study shows that human mobility patterns, despite short-term asymmetries, tend to exhibit effective equilibrium behavior at larger temporal scales, with a transition from asymmetric to balanced flows.

Contribution

It provides empirical evidence and a stochastic model demonstrating the emergence of effective detailed balance in human mobility at coarse temporal scales.

Findings

Over half of city pairs show flow balance at coarse scales

Flow imbalance decays as a power law with increasing time scale

Mobility fluctuations exhibit near-diffusive behavior

Abstract

A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by analyzing five years of intercity flow data covering millions of travelers. While short-term flows are highly asymmetric, temporal coarse-graining reveals that over half of all city pairs converge toward effective flow balance, with normalized directional imbalance decaying as a power law. The remaining pairs either exhibit persistent drift-dominated currents or a crossover between these two extremes. A stochastic model decomposing mobility into directional drift and correlated fluctuations quantitatively captures the coexistence of all three regimes. Directly measured variance scaling of the fluctuation process confirms near-diffusive behavior with regime-dependent deviations. These results demonstrate that large-scale mobility networks exhibit a scale-dependent transition from broken to restored flow symmetry, with direct implications for modeling transport and spreading dynamics.