Crowd behavior dynamics: entropic path-integral model

Vladimir G. Ivancevic

doi:10.1007/s11071-009-9544-6

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Crowd behavior dynamics: entropic path-integral model

2009-06-20

PRE

Vladimir G. Ivancevic *

Darryn J. Reid

Eugene Aidman

DOI：10.1007/s11071-009-9544-6

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Abstract

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We propose an entropic geometrical model of crowd behavior 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 (order parameter) is crowd entropy S that satisfies the Prigogine's extended second law of thermodynamics, a, (t) Sa parts per thousand yen0 (for any non-isolated 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, a, (t) S=0, while naturally chaotic crowd dynamics operates under (monotonically) increasing entropy function, a, (t) S > 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.

Keywords:

Crowd behavior dynamics

Action-amplitude formalism

Entropic crowd manifold

Crowd turbulence

Ricci flow

Topological phase transitions

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