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State Entropy and Differentiation Phenomenon

Liberal Arts Division, National Institute of Technology, Tokuyama College, Gakuendai, Shunan, Yamaguchi 745-8585, Japan
Department of Psychology, City University London, London EC1V 0HB, UK
International Center for Mathematical Modeling in Physics and Cognitive Sciences Linnaeus University, 351 95 Växjö-Kalmar, Sweden
National Research University of Information Technologies, Mechanics and Optics, St. Petersburg 197101, Russia
Author to whom correspondence should be addressed.
Entropy 2018, 20(6), 394;
Received: 5 April 2018 / Revised: 17 May 2018 / Accepted: 21 May 2018 / Published: 23 May 2018
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
PDF [437 KB, uploaded 23 May 2018]


In the formalism of quantum theory, a state of a system is represented by a density operator. Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy. It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement. To do this, we employ the model of differentiation, where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell’s differentiation, evolution of biological populations, and decision making. View Full-Text
Keywords: density operator; state entropy; von Neumann entropy; quantum measurement; differentiation density operator; state entropy; von Neumann entropy; quantum measurement; differentiation

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Asano, M.; Basieva, I.; Pothos, E.M.; Khrennikov, A. State Entropy and Differentiation Phenomenon. Entropy 2018, 20, 394.

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