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- Aerts, D., Czachor, M., Kuna, M., Sinervo, B. and Sozzo, S. (2014). Quantum probabilistic structures in competing lizard communities.
Ecological Modelling. Archive reference and link: http://arxiv.org/abs/1212.0109. download pdf.

Abstract:Almost two decades of research on the use of the mathematical formalism of quantum theory as 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 of human behavior and thought, such as in cognitive processes of decision-making, and in the way concepts are combined into sentences. In this paper, we extend this insight to animal behavior showing that a quantum probabilistic structure models the mating competition of three side-blotched lizard morphs. We analyze a set of experimental data collected from 1990 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 does not exist for the lizard's dynamics, and elaborate an explicit quantum description in Hilbert space faithfully modeling the gathered data. This result is relevant for population dynamics as a whole, since many systems, e.g. the so called plankton paradox situation, are believed to contain elements of cyclic competition.- Aerts, D. and Sassoli de Bianchi, M. (2014). The unreasonable success of quantum probability I: Quantum measurements as uniform fluctuations. Archive reference and link: http://arxiv.org/abs/1401.2647. download pdf.

Abstract:We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the Lebesgue-model can be further generalized into a model describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this more general framework we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article. In the second part, the proof of the equivalence between universal measurements and uniform measurements, and its significance for quantum theory as a first order approximation, is given and further analyzed.- Aerts, D. and Sassoli de Bianchi, M. (2014). The unreasonable success of quantum probability II: Quantum measurements as universal measurements. Archive reference and link: http://arxiv.org/abs/1401.2650. download pdf.

Abstract:We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the Lebesgue-model can be further generalized into a model describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this more general framework we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article. In the second part, the proof of the equivalence between universal measurements and uniform measurements, and its significance for quantum theory as a first order approximation, is given and further analyzed.

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