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Collective Motion from Quantum-Inspired Open Dynamics with Self-Perception Coupling: A Bloch Approximation Framework

Jyotiranjan Beuria

Abstract

In cognition, the perception of external stimuli and the self-referential awareness of one's own perceptual process are two distinct but interacting operations. We propose a quantum-inspired framework in which both the self state and the perception state are treated as coupled open quantum systems evolving across two different timescales. The fast perceptual subsystem captures adaptive sensing under coherent and dissipative influences, while the self subsystem evolves on a slower timescale, integrating perceptual feedback into a stable internal state. Their mutual coupling forms a closed informational loop, where the self-state biases perception, and perception continually reshapes the self. A macroscopic collective order emerges from the interplay of feedback, dissipation, and coherence. Although the Lindblad formalism rigorously captures microscopic quantum dynamics, the Bloch representation offers a far more tractable and intuitive description by compressing the evolution into observable quantities such as polarization, alignment, and coherence decay. Within this framework, we further identify several meaningful dynamical indicators, such as the collective order parameter, the degree of self-coherence, and the volitional inertia inferred from hysteresis-like loops, which together provide a quantitative characterization of emergent coordination and adaptation in a self-perception coupled system. Unlike traditional models of active matter that rely on instantaneous interaction rules, the introduction of an internal, slow-evolving self-subsystem integrates the history of perceptual interactions to capture adaptive and memory-dependent behavior.

Collective Motion from Quantum-Inspired Open Dynamics with Self-Perception Coupling: A Bloch Approximation Framework

Abstract

In cognition, the perception of external stimuli and the self-referential awareness of one's own perceptual process are two distinct but interacting operations. We propose a quantum-inspired framework in which both the self state and the perception state are treated as coupled open quantum systems evolving across two different timescales. The fast perceptual subsystem captures adaptive sensing under coherent and dissipative influences, while the self subsystem evolves on a slower timescale, integrating perceptual feedback into a stable internal state. Their mutual coupling forms a closed informational loop, where the self-state biases perception, and perception continually reshapes the self. A macroscopic collective order emerges from the interplay of feedback, dissipation, and coherence. Although the Lindblad formalism rigorously captures microscopic quantum dynamics, the Bloch representation offers a far more tractable and intuitive description by compressing the evolution into observable quantities such as polarization, alignment, and coherence decay. Within this framework, we further identify several meaningful dynamical indicators, such as the collective order parameter, the degree of self-coherence, and the volitional inertia inferred from hysteresis-like loops, which together provide a quantitative characterization of emergent coordination and adaptation in a self-perception coupled system. Unlike traditional models of active matter that rely on instantaneous interaction rules, the introduction of an internal, slow-evolving self-subsystem integrates the history of perceptual interactions to capture adaptive and memory-dependent behavior.

Paper Structure

This paper contains 18 sections, 25 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Framework
  3. Complete GKSL formulation
  4. Bloch reduction: deriving mean-field ODEs from the Lindblad equation
  5. Mean-field factorization.
  6. Unitary precession.
  7. Dissipative relaxation.
  8. Perceptual Bloch equations.
  9. Self Bloch equation (slow dynamics).
  10. Action-Perception operators and mapping to physical motion
  11. The Observables
  12. Bloch Mean Field related properties
  13. Global order parameters
  14. Self-perception correlation and phase lag
  15. Hysteresis and volitional inertia
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Self-Perception interaction framework that leads to macroscopic alignment and collective motion.
  • Figure 2: The temporal evolution of the collective order parameter or perceptual coherence $M(t)$ with the variations of $\Gamma$ and $\lambda_{\text{fb}}$.
  • Figure 3: The evolution of normalized covariance $C_{MS}$ and the phase lag $\Phi_{MS}$ between the macroscopic self variable $S(t)$ and the collective order parameter $M(t)$ with the variation of the feedback strength $\lambda_{\mathrm{fb}}$.
  • Figure 4: Hysteresis-like relationship between the equilibrium perceptual coherence $M^*$ and the equilibrium self coherence $S^*$ obtained from forward and backward sweeps of the feedback strength $\lambda_{\mathrm{fb}}$. The loop illustrates memory-dependent transitions emerging from the self-perception feedback dynamics.