用电路网络近似城市地区的人流：势场和涨落耗散关系
Approximation of human flow in urban areas by a network of electric circuits : Potential fields and fluctuation-dissipation relations
摘要：
由于大数据的出现，物理定律在非物质上的延伸已经取得了许多成功，人类流动是科学前沿课题之一。最近的全球定位系统技术已使追踪数百万人的详细轨迹成为可能，城市之间人流的重力定律等宏观方法和个人起点-目的地分布的微观方法正引起人们的极大关注。然而，要充分利用GPS数据实现大城市交通预测和城市规划，需要一个更通用、适用性更广的基础模型。在这里，基于一个新的想法，把移动的人作为带电粒子，我们引入了一个复杂的方法来映射宏观的人流量到电流上的一个假想的电路定义在一个大都市地区。电导被发现是几乎成比例的最大电流在每个位置和同步的人流在早上和晚上很好地描述了由电势的时间变化。令人惊讶的是，著名的涨落耗散定理成立，即电流的方差与类似于普通材料的电导率成正比。特别是在大流行期间，这种工具可为管理人员流动的决策提供宝贵的见解。
英文摘要：
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.
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