## Crowd Behavior Dynamics: Entropic Path–Integral Model (906)

### BibTeX

@MISC{Ivancevic906crowdbehavior,

author = {Vladimir G. Ivancevic and Darryn J. Reid and Eugene V. Aidman},

title = {Crowd Behavior Dynamics: Entropic Path–Integral Model},

year = {906}

}

### OpenURL

### 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.

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10 |
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9 | Generalized Hamiltonian biodynamics and topology invariants of humanoid robots - Ivancevic |

9 | Quantum noise, entanglement and chaos in the quantum field theory of mind-brain states - Pessa, Vitiello |

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Citation Context ...derivative along a geodesic and Ri jkm are the components of the Riemann curvature tensor of the CD manifold M. The relevant part of the Jacobi equation (43) is given by the tangent dynamics equation =-=[8, 5]-=- ¨J i + R i 0k0J k = 0, (i, k = 1, . . .,3n), (44) where the only non-vanishing components of the curvature tensor of the CD manifold M are R i 0k0 = ∂2 V/∂x i ∂x k . (45) The tangent dynamics equatio... |

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Citation Context ...derivative along a geodesic and Ri jkm are the components of the Riemann curvature tensor of the CD manifold M. The relevant part of the Jacobi equation (43) is given by the tangent dynamics equation =-=[8, 5]-=- ¨J i + R i 0k0J k = 0, (i, k = 1, . . .,3n), (44) where the only non-vanishing components of the curvature tensor of the CD manifold M are R i 0k0 = ∂2 V/∂x i ∂x k . (45) The tangent dynamics equatio... |

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Dynamical Systems Approaches to Cognition. In: Cambridge Handbook of Computational Cognitive Modeling
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6 |
Quantum noise induced entanglement and chaos in the dissipative quantum model of brain
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Citation Context ...e its degree of entanglement with the other subsystems. The most popular issue in a research on dissipative quantum brain modelling has been quantum entanglement between the brain and its environment =-=[65, 66]-=-, where the brain–environment system has an entangled ‘memory’ state, identified with the ground (vacuum) state |0 >N , that cannot be factorized into two single–mode states. (In the Vitiello–Pessa di... |