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Owing to the big data the extension of physical laws on nonmaterial has seennumerous successes, and human mobility is one of the scientific frontiertopics. Recent GPS technology has made it possible to trace detailedtrajectories of millions of people, macroscopic approaches such as the gravitylaw for human flow between cities and microscopic approaches of individualorigin-destination distributions are attracting much attention. However, weneed a more general basic model with wide applicability to realize trafficforecasting and urban planning of metropolis fully utilizing the GPS data.Here, based on a novel idea of treating moving people as charged particles, weintroduce a sophisticated method to map macroscopic human flows into currentson an imaginary electric circuit defined over a metropolitan area. Conductanceis found to be nearly proportional to the maximum current in each location andsynchronized human flows in the morning and evening are well described by thetemporal changes of electric potential. Surprisingly, the famous fluctuationdissipation theorem holds, namely, the variances of currents are proportionalto the conductivities akin to an ordinary material. Especially during thepandemic, such a tool may offer an invaluable insight for policy-making inmanaging human flows.

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