Paper: arXiv 2306.15554

Authors: Leilei Shi, Xinshuai Guo, Jiuchang Wei, Wei Zhang, Guocheng Wang, Bing-Hong Wang

Abstract

Complex adaptive learning is intelligent. It is adaptive, learns in feedback loops, and generates hidden patterns as many individuals, elements or particles interact in complex adaptive systems (CAS). CAS highlights adaptation in life and lifeless complex systems cutting across all traditional natural and social sciences disciplines. However, discovering a universal law in CAS and understanding the underlying mechanism of distribution formation, such as a non-Gauss distribution in complex quantum entanglement, remains highly challenging. Quantifying the uncertainty of CAS by probability wave functions, the authors explore the inherent logical relationship between Schrödinger’s wave equation in quantum mechanics and Shi’s trading volume-price wave equation in finance. Subsequently, the authors propose a non-localized wave equation in quantum mechanics if cumulative observable in a time interval represents momentum or momentum force in Skinner-Shi (reinforcement-frequency-interaction) coordinates. It reveals that the invariance of interaction as a universal law exists in quantum mechanics and finance. The theory shows that quantum entanglement is an interactively coherent state instead of a consequence of the superposition of coherent states. As a resource, quantum entanglement is non-separable, steerable, and energy-consumed. The entanglement state has opposite states subject to interaction conservation between the momentum and reversal forces. Keywords: complex adaptive systems, complex adaptive learning, complex quantum systems, non-localized wave equation, interaction conservation, interactively coherent entanglement PACS: 89.75.-k (Complex Systems); 89.65.Gh (Economics, Econophysics, Financial Markets, Business and Management); 03.65.Ud (Entanglement and Quantum Nonlocality)

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents an ambitious theoretical framework bridging quantum mechanics wave equations and financial volume-price dynamics. While mathematically rich and highly novel in its econophysics cross-disciplinary approach, it lacks empirical backtesting, data validation, and practical reproducibility for quant trading applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Discover Universal Law in CAS & Explain Quantum Entanglement Dynamics] --> B[Input Data/Concepts: Skinner-Shi Coordinates, Schrödinger Wave Equation & Trading Volume-Price Dynamics]
    B --> C[Methodology: Quantify CAS Uncertainty via Probability Waves Across Finance & Quantum Physics]
    C --> D[Computational Process: Derive Non-Localized Wave Equation using Cumulative Observables for Momentum Forces]
    D --> E[Outcome 1: Prove Invariance of Interaction Conservation Across Quantum Mechanics & Finance]
    D --> F[Outcome 2: Define Quantum Entanglement as an Interactively Coherent, Non-Separable & Energy-Consuming State]