Entropic Geometry of Crowd Dynamics

Abstract

In this Chapter we propose a nonlinear entropic model of crowd generic psycho-physical 1 dynamics. For this we use Feynman's action-amplitude formalism, operating on microscopic, mesoscopic and macroscopic synergetic levels, which correspond to individual, group (aggregate) and full crowd behavior dynamics, respectively. In all three levels, goaldirected behavior operates under entropy conservation, t S = 0, while naturally chaotic behavior operates under (monotonically) increasing entropy, t S > 0. Between these two distinct behavioral phases lies a topological phase transition with a chaotic inter-phase. We formulate a geometrical representation of this behavioral transition in terms of the Perelman-Ricci flow on the crowd's Riemannian configuration manifold. Recall that in psychology the term cognition 2 refers to an information processing view of an individual psychological functions (see [3; 4; 68; 81; 88]). More generally, cognitive processes can be natural and artificial, conscious and not conscious; therefore, they are analyzed from different perspectives and in different contexts, e.g., anesthesia, neurology, psychology, philosophy, logic (both Aristotelian and mathematical), systemics, computer science, artificial intelligence (AI) and computational intelligence (CI). Both in psychology and in AI/CI, cognition refers to the mental functions, mental processes and states of intelligent entities (humans, human organizations, highly autonomous robots), with a particular focus toward the study of comprehension, inferencing, decision-making, planning and learning (see, e.g. The recently developed Scholarpedia, the free peer reviewed web encyclopedia of computational neuroscience is largely based on cognitive neuroscience (see, e.g. The concept of cognition is closely related to such abstract concepts as mind, reasoning, perception, intelligence, learning, and many others that describe numerous capabilities of the human mind and expected properties of AI/CI (see [51; 57] and references therein). Yet disembodied cognition is a myth, albeit one that has had profound influence in Western science since Rene Descartes and others gave it credence during the Scientific Revolution. In fact, the mind-body separation had much more to do with explanation of method than with explanation of the mind and cognition, yet it is with respect to the latter that its impact is most widely felt. We find it to be an unsustainable assumption in the realm of crowd behavior.