  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.
