Hubsch, T., Minic, D., Nikolic, Konstantin ORCID: https://orcid.org/0000-0002-6551-2977 and Pajevic, S. (2024) On the emergent “Quantum” theory in complex adaptive systems. Annals of Physics, 464.

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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 Schrodinger-type equation, with a (mock) Planck constant , which is system-dependent. The condition for this is that the so-called quantum potential
, which is state-dependent, is canceled 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
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 particular, we present a general argument as to why the non-equilibrium dynamics of a classical system could lead to a mock quantum description that ensures stability compatible with adaptability. 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 re-frame 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.

Item Type:	Article
Identifier:	10.1016/j.aop.2024.169641
Subjects:	Computing > Systems
Depositing User:	Konstantin Nikolic
Date Deposited:	16 Sep 2024 14:05
Last Modified:	04 Nov 2024 11:00
URI:	https://repository.uwl.ac.uk/id/eprint/12451

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