On the Emergent "Quantum" Theory in Complex Adaptive Systems

TL;DR

This paper investigates the possibility of emergent quantum-like behavior in complex adaptive systems, especially biological ones, by reformulating classical dynamics into a quantum-like formalism and exploring conditions for stable, stationary states.

Contribution

It introduces the concept of mock quantum theory in classical systems, detailing how quantum formalism can emerge through environment coupling and fine-tuning, with implications for understanding biological stability.

Findings

Classical systems can be reformulated into a Schrödinger-like equation with a system-dependent mock Planck constant.

Conditions for canceling the quantum potential involve coupling to the environment, enabling stable states.

The transition from quantum to classical can be viewed as a form of quantum turbulence, analogous to hydrodynamic flow transitions.

Abstract

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or "mock") quantum theory in the Lotka-Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton-Jacobi (HJ) equation and reduce it to an effective Schr\"odinger-type equation, with a (mock) Planck constant $\mockbar$, which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is cancelled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the "environment." We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we reframe the concept of decoherence into the concept of "quantum turbulence," i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.