Are Words the Quanta of Human Language? Extending the Domain of Quantum Cognition

In previous research, we showed that ‘texts that tell a story’ exhibit a statistical structure that is not Maxwell–Boltzmann but Bose–Einstein. Our explanation is that this is due to the presence of ‘indistinguishability’ in human language as a result of the same words in different parts of the story being indistinguishable from one another, in much the same way that ’indistinguishability’ occurs in quantum mechanics, also there leading to the presence of Bose–Einstein rather than Maxwell–Boltzmann as a statistical structure. In the current article, we set out to provide an explanation for this Bose–Einstein statistics in human language. We show that it is the presence of ‘meaning’ in ‘texts that tell a story’ that gives rise to the lack of independence characteristic of Bose–Einstein, and provides conclusive evidence that ‘words can be considered the quanta of human language’, structurally similar to how ‘photons are the quanta of electromagnetic radiation’. Using several studies on entanglement from our Brussels research group, we also show, by introducing the von Neumann entropy for human language, that it is also the presence of ‘meaning’ in texts that makes the entropy of a total text smaller relative to the entropy of the words composing it. We explain how the new insights in this article fit in with the research domain called ‘quantum cognition’, where quantum probability models and quantum vector spaces are used in human cognition, and are also relevant to the use of quantum structures in information retrieval and natural language processing, and how they introduce ‘quantization’ and ‘Bose–Einstein statistics’ as relevant quantum effects there. Inspired by the conceptuality interpretation of quantum mechanics, and relying on the new insights, we put forward hypotheses about the nature of physical reality. In doing so, we note how this new type of decrease in entropy, and its explanation, may be important for the development of quantum thermodynamics. We likewise note how it can also give rise to an original explanatory picture of the nature of physical reality on the surface of planet Earth, in which human culture emerges as a reinforcing continuation of life.     

Land cover change using an energy transition paradigm in a statistical mechanics approach

This paper explores a statistical mechanics approach as a means to better understand specific land cover changes on a continental scale. Integrated assessment models are used to calculate the impact of anthropogenic emissions via the coupling of technoeconomic and earth/atmospheric system models and they have often overlooked or oversimplified the evolution of land cover change. Different time scales and the uncertainties inherent in long term projections of land cover make their coupling to integrated assessment models difficult. The mainstream approach to land cover modelling is rule-based methodology and this necessarily implies that decision mechanisms are often removed from the physical geospatial realities, therefore a number of questions remain: How much of the predictive power of land cover change can be linked to the physical situation as opposed to social and policy realities? Can land cover change be understood using a statistical approach that includes only economic drivers and the availability of resources? In this paper, we use an energy transition paradigm as a means to predict this change. A cost function is applied to developed land covers for urban and agricultural areas. The counting of area is addressed using specific examples of a Pólya process involving Maxwell–Boltzmann and Bose–Einstein statistics. We apply an iterative counting method and compare the simulated statistics with fractional land cover data with a multi-national database. An energy level paradigm is used as a basis in a flow model for land cover change. The model is compared with tabulated land cover change in Europe for the period 1990–2000. The model post-predicts changes for each nation. When strong extraneous factors are absent, the model shows promise in reproducing data and can provide a means to test hypothesis for the standard rules-based algorithms.     

Fluctuations in the Bose Gas with Attractive Boundary Conditions

In this paper limiting distribution functions of field and density fluctuations are explicitly and rigorously computed for the different phases of the Bose gas. Several Gaussian and non-Gaussian distribution functions are obtained and the dependence on boundary conditions is explicitly derived. The model under consideration is the free Bose gas subjected to attractive boundary conditions, such boundary conditions yield a gap in the spectrum. The presence of a spectral gap and the method of the coupled thermodynamic limits are the new aspects of this work, leading to new scaling exponents and new fluctuation distribution functions.     

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose–Einstein condensation are discussed.     

A Modified Boltzmann Equation for Bose–Einstein Particles: Isotropic Solutions and Long-Time Behavior

Under some strong cutoff conditions on collision kernels, global existence, local stability, entropy identity, conservation of energy, and moment production estimates are proven for isotropic solutions of a modified (quantum effect) Boltzmann equation for spatially homogeneous gases of Bose–Einstein particles (BBE). Then applying these results with the biting-weak convergence, some results on the long-time behavior of the conservative isotropic solutions of the BBE equation are obtained, including the velocity concentration at very low temperatures and the tendency toward equilibrium states at very high temperatures.