Trip flow between areas is a fundamental metric for human mobility research. Given its identification with travel demand and its relevance for transportation and urban planning, many models have been developed for its estimation. These models focus on flow intensity, disregarding the information provided by the local mobility orientation. A field-theoretic approach can overcome this issue and handling both intensity and direction at once. Here we propose a general vector-field representation starting from individuals' trajectories valid for any type of mobility. By introducing four models of spatial exploration, we show how individuals' elections determine the mesoscopic properties of the mobility field. Distance optimization in long displacements and random-like local exploration are necessary to reproduce empirical field features observed in Chinese logistic data and in New York City Foursquare check-ins. Our framework is an essential tool to capture hidden symmetries in mesoscopic urban mobility, it establishes a benchmark to test the validity of mobility models and opens the doors to the use of field theory in a wide spectrum of applications.

翻译：区域间出行流量是衡量人类移动性的基本指标。鉴于其与出行需求的一致性及其对交通与城市规划的重要性，已有大量模型被开发用于其估算。这些模型侧重于流量强度，忽略了局部移动方向所提供的信息。场论方法能够克服这一局限，同时处理强度与方向。本文提出一种基于个体轨迹的广义矢量场表示，该方法适用于任意类型的移动性。通过引入四种空间探索模型，我们展示了个体的选择如何决定移动场的介观性质。长距离位移中的距离优化与类随机局部探索是再现中国物流数据及纽约市Foursquare签到数据中观测到的经验场特征的必要条件。我们的框架是捕捉城市介观移动性中隐藏对称性的核心工具，它为验证移动性模型的有效性建立了基准，并为场论在广泛领域的应用开辟了道路。