Field theory for recurrent mobility

TL;DR

This paper introduces a field theory approach to human mobility, demonstrating that daily commuting flows form irrotational vector fields that can be modeled analytically, aiding urban planning and epidemic forecasting.

Contribution

It reveals that commuting flows form divergence-free, irrotational vector fields and introduces a potential-based framework for delineating urban mobility basins, validated by gravity models.

Findings

Commuting flows form irrotational vector fields obeying divergence theorem.

Empirical fluxes and potentials are well reproduced by gravity models.

Intervening opportunities models struggle to replicate observed flows.

Abstract

Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the pervasive adoption of mobile technologies has brought a wealth of (real time) data. The easy access to this information opens the door to study theoretical questions so far unexplored. In this work, we show for a series of worldwide cities that commuting daily flows can be mapped into a well behaved vector field, fulfilling the divergence theorem and which is, besides, irrotational. This property allows us to define a potential for the field that can become a major instrument to determine separate mobility basins and discern contiguous urban areas. We also show that empirical fluxes and potentials can be well reproduced and analytically characterized using the so-called gravity model, while other models based on intervening opportunities have serious difficulties.