群体动力学的熵几何
Entropic Geometry of Crowd Dynamics
摘要：
我们提出了一个熵的几何模型的心理-物理群体动力学（耗散群体运动学），使用费曼动作振幅形式主义，在三个协同水平：宏观，中观和微观。其目的是解释人群的动态同时和一致的这三个层次，以表征其几何特性，特别是相对于行为制度和它们之间的状态变化。其最自然的统计描述符是满足Prigogine热力学扩展第二定律的拥挤熵$S$，$\partial_tS\geq 0$（适用于任何非孤立的多组分系统）。个人和人群配置流形之间的定性相似性和叠加激发了我们的主张，即目标导向的人群运动在熵守恒下运行，$\partial_tS = 0$，而自然的人群动力学在（单调）增加的熵函数下运行，$\partial_tS > 0$。在这两个不同的拓扑相位之间存在着一个具有混沌相间的相变。惯性群体动力学和耗散运动学都表示由Ricci流控制的群体流形上的扩散过程，以及相关的Perelman熵作用。关键词：群体心理物理动力学，作用振幅形式，群体流形，Ricci流，Perelman熵，拓扑相变
英文摘要：
We propose an entropic geometrical model of psycho-physical crowd dynamics (with dissipative crowd kinematics), using Feynman action-amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to explain the dynamics of crowds simultaneously and consistently across these three levels, in order to characterize their geometrical properties particularly with respect to behavior regimes and the state changes between them. Its most natural statistical descriptor is crowd entropy $S$ that satisfies the Prigogine's extended second law of thermodynamics, $\partial_tS\geq 0$ (for any nonisolated multi-component system). Qualitative similarities and superpositions between individual and crowd configuration manifolds motivate our claim that goal-directed crowd movement operates under entropy conservation, $\partial_tS = 0$, while natural crowd dynamics operates under (monotonically) increasing entropy function, $\partial_tS > 0$. Between these two distinct topological phases lies a phase transition with a chaotic inter-phase. Both inertial crowd dynamics and its dissipative kinematics represent diffusion processes on the crowd manifold governed by the Ricci flow, with the associated Perelman entropy-action. Keywords: Crowd psycho-physical dynamics, action-amplitude formalism, crowd manifold, Ricci flow, Perelman entropy, topological phase transition
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