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Population dynamics of entangled species

Bar Y. Peled, Amit Te’eni, Eliahu Cohen, Avishy Y. Carmi

Published Sep 9, 2021• 0 citations
OpenAlex

Abstract

The laws of physics enter the doctrine of population dynamics through various interactions whereby energy and matter, or more broadly, information are exchanged between different species and between species and their natural environment. The dynamics then emerge as a continual process involving many such causal interactions. Quantum physics, on the other hand, shows that the coordination between different processes must obey certain rules. We hypothetically ask: Can this game of species benefit from unique features of quantum mechanics such as entanglement and nonlocality? Here we extend quantum game theory to analyze this question and demonstrate that in certain models describing ecological systems where several predators feed on the same prey, the strength of quantum entanglement between the various species has a profound effect on the asymptotic behavior of the system. For example, if there are sufficiently many predator species who are all equally correlated with their prey, they are all driven to extinction. These results were derived in two ways: by analyzing the asymptotic dynamics of the system, and also by modeling the system as a quantum correlation network, which enabled us to apply methods from network theory in the above scenarios. Several generalizations and applications are discussed.

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The laws of physics enter the doctrine of population dynamics through various interactions whereby energy and matter, or more broadly, information are exchanged between different species and between species and their natural environment. The dynamics then emerge as a continual process involving many such causal interactions. Quantum physics, on the other hand, shows that the coordination between different processes must obey certain rules. We hypothetically ask: Can this game of species benefit from unique features of quantum mechanics such as entanglement and nonlocality? Here we extend quantum game theory to analyze this question and demonstrate that in certain models describing ecological systems where several predators feed on the same prey, the strength of quantum entanglement between the various species has a profound effect on the asymptotic behavior of the system. For example, if there are sufficiently many predator species who are all equally correlated with their prey, they are all driven to extinction. These results were derived in two ways: by analyzing the asymptotic dynamics of the system, and also by modeling the system as a quantum correlation network, which enabled us to apply methods from network theory in the above scenarios. Several generalizations and applications are discussed.
At both conceptual and applied levels, quantum physics provides new opportunities as well as fundamental limitations. We hypothetically ask whether quantum games inspired by population dynamics can benefit from unique features of quantum mechanics such as entanglement and nonlocality. For doing so, we extend quantum game theory and demonstrate that in certain models inspired by ecological systems where several predators feed on the same prey, the strength of quantum entanglement between the various species has a profound effect on the asymptotic behavior of the system. For example, if there are sufficiently many predator species who are all equally correlated with their prey, they are all driven to extinction. Our results are derived in two ways: by analyzing the asymptotic dynamics of the system, and also by modeling the system as a quantum correlation network. The latter approach enables us to apply various tools from classical network theory in the above quantum scenarios. Several generalizations and applications are discussed.
By incorporating payoff matrix and population evolution of open systems and proposing density games, pioneering effort has been made to break the following two basic assumptions of evolutionary game theory over the past decades: the payoff from the game determines the reproductive rate of individuals, and the total population size remains constant by a variable called the death rate. On the other hand, most studies on strategic interactions in game theories consider independent individual strategies as the basic unit of analyses. This is in fact not always true in human interaction strategies. It has been unclear that how subjective non-independent species with strategic interactions in open dynamic systems evolve. In this paper, we create the new concept of hybrid quantum games, and propose an open quantum dynamic symbiosis model for exploring the evolution of this type of species under unclosed social settings. We show that the stability conditions of the model with non-independent strategic interactions are influenced by the specific symbiosis states, game payoff matrix and quantum entanglement. The stability conditions of the competition scenario are more stringent than those of the cooperation one. Our system dynamics simulation study demonstrates and verifies the dynamic changes for the population sizes of two different species in the theoretical model, on the basis of the stability conditions of the competition and cooperation scenarios. Our model combines quantum games, game payoff matrix and symbiosis equations organically, and can provide insights into competition, cooperation and symbiosis mechanisms in open systems with subjective non-independent strategies considered.
Population ecology is mainly based on nonlinear equations of the Lotka-Volterra type, which provide mathematical models for describing the dynamics of interacting species. However, for many interacting populations, these equations entail complex dynamical behavior and unpredictability, generating such difficulties and problematical situations as illustrated by the 'paradox of the plankton' and the 'paradox of enrichment', for instance. A careful analysis shows that an ecosystem is a fundamentally contextual system, hence any formalism describing such systems should incorporate contextuality from the very beginning. But existing approaches are based on classical physics and probability theory, and introduce contextuality as an external effect, so that they cannot generally explain the main peculiarities of ecosystems. Basing ourselves on a contextual formalism elaborated to study microscopic systems in quantum mechanics and including appropriate nonlinear equations, we construct a generalization of the Lotka-Volterra equations for contextual systems, apply these equations to discuss some paradoxical situations encountered in ecology, and propound alternative solutions to those currently existing in the literature.
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be used to explain more correctly biological and economical processes and even it could encloses theories like games and evolutionary dynamics. This could make quantum mechanics a more general theory that we had thought. Although both systems analyzed are described through two apparently different theories (quantum mechanics and game theory) it is shown that both systems are analogous and thus exactly equivalents. So, we can take some concepts and definitions from quantum mechanics and physics for the best understanding of the behavior of economics and biology. Also, we could maybe understand nature like a game in where its players compete for a common welfare and the equilibrium of the system that they are members.
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.
Quantum information science has altered the concept of the method of processing and transporting information through the laws of quantum mechanics. Quantum entanglement is one of its basic properties, which is instrumental to non-classical correlations between spatially separate particles. New quantum communication networks and quantum computing systems distributed are based on these interrelations. In this paper, quantum information flow dynamics of multi-particle entangled networks with particular emphasis to the processes governing information transmission, redistribution and maintenance of coupled quantum nodes are discussed. The paper discloses the way in which the entangled structures comprising multiple entities can help in facilitating the sharing of information beyond the capabilities of the classical communication systems. Complex entangled structures are analyzed in terms of the channels through which the flow of quantum information is analyzed in respect to the theoretical models of multi-qubit systems and networked quantum channels. The way the communication between the particles influences the coherence, strength of correlation, as well as the stability of the whole network in general, is given particular attention. The effect of environmental noise and decoherence which can cause a break of entanglement and the loss of efficiency in quantum information exchange is also considered in the analysis. Moreover, the article discusses the application of network topology in order to establish the behaviour of entangled systems. The impact of the structural changes on information transfer reliability and speed is determined by the evaluation of the various forms of quantum nodes and connections. These findings suggest that entangled networks structured appropriately will be able to enhance stability of quantum communication and assist in distributing quantum resources more efficiently. Overall, the present research can be deemed as part of the bigger initiative of scaling up quantum communication infrastructures. The research builds knowledge in the sense that it provides an insight into the behavior of information in multi-particle entangled networks with important considerations being made as to the advancement of robust quantum networks which can be used in future to support the realization of future applications in the area of secure communication, distributed computing and the future developments in information processing technologies.