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On the Emergent "Quantum" Theory in Complex Adaptive Systems.

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    Complex adaptive systems can exhibit emergent quantum-like theories. This study shows how classical systems can mimic quantum mechanics, potentially explaining stable states in biological systems through "quantum turbulence".

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    Area of Science:

    • Theoretical Physics
    • Complex Systems
    • Mathematical Biology

    Background:

    • Classical systems are typically described by deterministic equations like the Hamilton-Jacobi (HJ) equation.
    • Emergent quantum-like phenomena in classical systems remain an area of theoretical exploration.
    • Understanding transitions from quantum to classical behavior is crucial in physics and complex systems.

    Purpose of the Study:

    • To investigate the possibility of implementing quantum mechanics formalism on classical systems.
    • To explore emergent quantum-like theories in complex adaptive systems, using the Lotka-Volterra system as a case study.
    • To introduce the concept of mock quantum statistical field theory and reframe decoherence as quantum turbulence.

    Main Methods:

    • Reducing the classical Hamilton-Jacobi equation to an effective Schr"odinger-type equation with a system-dependent mock Planck constant.
    • Analyzing the conditions under which the state-dependent quantum potential (VQ) is canceled out by an environmental coupling term.
    • Utilizing a hydrodynamic formulation to study the transition from mock quantum to classical behavior, analogous to laminar-to-turbulent flow.

    Main Results:

    • A classical system can be reduced to an effective Schr"odinger-type equation if the quantum potential is canceled.
    • The cancellation of the quantum potential can be achieved through environmental coupling and fine-tuning, potentially leading to stable states in adaptive systems.
    • A novel concept of mock quantum, state-dependent, statistical field theory is introduced.
    • The quantum-to-classical transition is reframed as "quantum turbulence," analogous to hydrodynamics.

    Conclusions:

    • Classical systems can exhibit emergent quantum-like behaviors under specific conditions, offering new perspectives on complex adaptive systems.
    • Environmental coupling and fine-tuning play a critical role in enabling classical systems to mimic quantum dynamics.
    • The concept of quantum turbulence provides a novel framework for understanding the transition from quantum to classical regimes.