Crowd behavior dynamics: entropic path-integral model

Abstract

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, ∂tS ≥ 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, ∂tS = 0, while naturally chaotic crowd dynamics operates under (monotonically) increasing entropy function, ∂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.

Action-Amplitude Approach to Controlled Entropic Self-Organization

“…In this way, we arrive at our main conceptual tool, the geometrical/topological path integral, in its Euclidean and Lorentzian versions, respectively given by (see [3]):…”

“…The path integral Equations (17) and (18) are constructed, respectively, from the classical behavioral actions (see [3]):…”

“…From these cases, the set of discrete Euler-Lagrangian equations of motion on the group/graph, Γ, can be derived (see [3], as well as Section 3 below). Geometrically, this means that the perceptual error, in all three forms-the absolute value (1), the L 2 -norm (3)-(5), or the metric (4)-(6)-represents an energy landscape.…”

The chaotic dynamics of the social behavior selection networks in crowd simulation

“…Crowd simulation [1][2][3][4][5][6][7][8][9] is an interesting field that focuses on all processes related to emergence, change, evolution, interactions, and extinction of crowd behavior that was researched since 1896 [10]. Crowd dynamic simulation includes the modeling of crowd behaviors, behavioral switch dynamics, and their interaction with the people around them and the social, physical environment.…”

Dynamics of confined crowds modelled using Entropic Stochastic Resonance and Quantum Neural Networks

“…In this paper, we present an approach to modelling dynamics of confined crowds (or aggregates, see Ivancevic et al, 2010;) driven by ESR. This confined crowd dynamics resembles nonlinear system dynamics defined by kinetic equations (1), (3) and (4) below.…”