Department of Biology and Evolutionary BiologyUniversity of California, Santa Cruz, California, USAEmail: lizardrps@gmail.comAbstractAlmost two decades of research on the use of the mathematical formalism of quantum theoryas a modeling tool for entities and their dynamics in domains different from the micro-world has now firmly shown the systematic appearance of quantum structures in aspects ofhuman behavior and thought, such as in cognitive processes of decision-making, and in theway concepts are combined into sentences. In this paper, we extend this insight to animalbehavior showing that a quantum probabilistic structure models the mating competition ofthree side-blotched lizard morphs. We analyze a set of experimental data collected from1990 to 2011 on these morphs, whose territorial behavior follows a cyclic rock-paper-scissors(RPS) dynamics. Consequently we prove that a single classical Kolmogorovian space doesnot exist for the lizard’s dynamics, and elaborate an explicit quantum description in Hilbertspace faithfully modeling the gathered data. This result is relevant for population dynamicsas a whole, since many systems, e.g. the so called plankton paradox situation, are believedto contain elements of cyclic competition.
Department of Biology and Evolutionary BiologyUniversity of California, Santa Cruz, California, USAEmail: lizardrps@gmail.comAbstractAlmost two decades of research on the use of the mathematical formalism of quantum theoryas a modeling tool for entities and their dynamics in domains different from the micro-world has now firmly shown the systematic appearance of quantum structures in aspects ofhuman behavior and thought, such as in cognitive processes of decision-making, and in theway concepts are combined into sentences. In this paper, we extend this insight to animalbehavior showing that a quantum probabilistic structure models the mating competition ofthree side-blotched lizard morphs. We analyze a set of experimental data collected from1990 to 2011 on these morphs, whose territorial behavior follows a cyclic rock-paper-scissors(RPS) dynamics. Consequently we prove that a single classical Kolmogorovian space doesnot exist for the lizard’s dynamics, and elaborate an explicit quantum description in Hilbertspace faithfully modeling the gathered data. This result is relevant for population dynamicsas a whole, since many systems, e.g. the so called plankton paradox situation, are believedto contain elements of cyclic competition.
Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing that an analysis of an interactive situation involving a mating competition between certain lizard morphs allows to identify a quantum theoretic structure. More in particular, we show that when this lizard competition is analyzed structurally in the light of a compound entity consisting of subentities, the contextuality provided by the presence of an underlying rock-paper-scissors cyclic dynamics leads to a violation of Bell's inequality, which means it is of a non-classical type. We work out an explicit quantum-mechanical representation in Hilbert space for the lizard situation and show that it faithfully models a set of experimental data collected on three throat-colored morphs of a specific lizard species. Furthermore, we investigate the Hilbert space modeling, and show that the states describing the lizard competitions contain entanglement for each one of the considered confrontations of lizards with different competing strategies, which renders it no longer possible to interpret these states of the competing lizards as compositions of states of the individual lizards.
Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
Abstract Despite predictive success, population dynamics and evolutionary game theory still pose fundamental problems. Violation of the competitive exclusion principle in plankton communities provides an example. A promising solution of this ‘paradox of the plankton’ comes from theories involving cyclic competition, an evolutionary analogue of the classical rock-paper-scissors (RPS) game. However, modeling probabilistic RPS structures, one encounters a fundamental difficulty: the pairs rock-scissors, scissors-paper, and paper-rock possess representations in separate Kolmogorovian probability spaces, but a single global probability space for entire triplets does not exist. Populations that take part in cyclic competition should therefore involve probabilistic incompatibilities, analogous to those occurring in quantum mechanics. Here, using experimental data collected from 1990 to 2011 on the RPS cycles of lizards, we show that the incompatibilities are indeed unavoidable, and the data cannot be reconstructed from a single Kolmogorovian probability space. We then prove that the effect is genuinely quantum probabilistic, i.e. all the probabilities can be formulated in terms of a single density matrix and a set of non-commuting projectors. This formal quantum structure is dormant in games where probabilities of strategies do not entangle with probabilities of payoffs, and thus could be overlooked. In more realistic scenarios, involving games ‘with ace in a sleeve’, the non-Kolmogorovian structure can be activated. Surprisingly, lizards occasionally do play such games. In consequence, the formalism of evolutionary games, similarly to quantum mechanics, should begin with density matrix equations. Implications of our finding extend beyond lizard communities, given that RPS games are common in nature and higher dimensional RPS games may be even more common in ecosystems.
Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a diverse range of macroscopic systems both within and outside of physics. This book describes how complex systems from a variety of fields can be modelled using quantum mechanical principles; from biology and ecology, to sociology and decision-making. The mathematical basis of these models is covered in detail, furnishing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. It will be an essential resource for students and researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to dynamical systems in the social, biological or ecological sciences.
Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, interference and superposition in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.
Quantum entanglement, a phenomenon where two or more particles become linked and share the same fate, has captivated physicists and philosophers alike. While established in quantum mechanics, its application to complex systems, particularly cellular automata, presents a fascinating challenge and opportunity. This paper explores the potential of extending the concept of quantum entanglement beyond individual particles to propose a dynamic, multi-level entanglement structure within cellular automata simulations. We hypothesize that this approach, driven by chaotic behavior observed in cellular automata, could yield emergent phenomena, including "quantum foam" behavior, offering novel insights into the fundamental nature of reality. The core mechanism involves introducing a novel evolution rule based on chaotic dynamics, incorporating feedback loops and probabilistic branching to generate complex entanglement patterns. This work aims to advance our understanding of entanglement's role in complex systems and potentially lead to new computational models.