Approximation of human flow in urban areas by a network of electric circuits : Potential fields and fluctuation-dissipation relations

TL;DR

This paper models urban human mobility by mapping large-scale GPS data onto an electric circuit analogy, revealing that human flows follow physical laws like fluctuation-dissipation relations, aiding urban planning and policy-making.

Contribution

It introduces a novel approach treating human movement as electric currents, applying physical laws to analyze and predict urban human flow patterns.

Findings

Human flows correlate with electric potential changes over time.

Conductance is nearly proportional to maximum current at locations.

Fluctuation-dissipation theorem applies to human mobility data.

Abstract

Owing to the big data the extension of physical laws on nonmaterial has seen numerous successes, and human mobility is one of the scientific frontier topics. Recent GPS technology has made it possible to trace detailed trajectories of millions of people, macroscopic approaches such as the gravity law for human flow between cities and microscopic approaches of individual origin-destination distributions are attracting much attention. However, we need a more general basic model with wide applicability to realize traffic forecasting and urban planning of metropolis fully utilizing the GPS data. Here, based on a novel idea of treating moving people as charged particles, we introduce a sophisticated method to map macroscopic human flows into currents on an imaginary electric circuit defined over a metropolitan area. Conductance is found to be nearly proportional to the maximum current in each location and synchronized human flows in the morning and evening are well described by the temporal changes of electric potential. Surprisingly, the famous fluctuation dissipation theorem holds, namely, the variances of currents are proportional to the conductivities akin to an ordinary material. Especially during the pandemic, such a tool may offer an invaluable insight for policy-making in managing human flows.