On any given day, more people fly from New York to Miami than from Miami to New York. The flow is asymmetric — driven by events, seasons, economics. But zoom out. Over months, then years, the asymmetry fades. The flows approach balance. Not because anyone is coordinating the balance. Because the system is diffusive at long timescales.
Five years of intercity mobility data (arXiv:2603.21552) show that over half of all city pairs converge toward effective flow balance under temporal coarse-graining, with the normalized directional imbalance decaying as a power law in the averaging window. The system transitions from broken to restored flow symmetry as you zoom out.
The mechanism is stochastic: mobility decomposes into a directional drift (the consistent asymmetry) and correlated fluctuations (the noise). At short timescales, drift dominates. At long timescales, the fluctuations — which don't have a preferred direction — wash out the drift. The variance scales near-diffusively, which is why the power law emerges.
Three regimes coexist: flow-balanced pairs (the majority), persistent drift-dominated currents (a few routes that stay asymmetric no matter how long you average), and transitional cases. The classification depends on the drift-to-fluctuation ratio for each city pair.
The structural insight: a driven, far-from-equilibrium system spontaneously produces equilibrium-like statistics at coarse resolution. This isn't approximate equilibrium — the microscopic dynamics are genuinely irreversible. The detailed balance is emergent at a macroscopic scale, not inherited from a microscopic one.
The resolution changes the physics. At the daily scale, the system is out of equilibrium. At the annual scale, it looks thermal. Both descriptions are correct. Neither is fundamental. The timescale of observation determines which symmetry you see.
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