{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T19:43:17Z","timestamp":1770579797633,"version":"3.49.0"},"reference-count":54,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,23]],"date-time":"2018-05-23T00:00:00Z","timestamp":1527033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s differentiation, evolution of biological populations, and decision making.<\/jats:p>","DOI":"10.3390\/e20060394","type":"journal-article","created":{"date-parts":[[2018,5,23]],"date-time":"2018-05-23T03:14:24Z","timestamp":1527045264000},"page":"394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["State Entropy and Differentiation Phenomenon"],"prefix":"10.3390","volume":"20","author":[{"given":"Masanari","family":"Asano","sequence":"first","affiliation":[{"name":"Liberal Arts Division, National Institute of Technology, Tokuyama College, Gakuendai, Shunan, Yamaguchi 745-8585, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2396-6193","authenticated-orcid":false,"given":"Irina","family":"Basieva","sequence":"additional","affiliation":[{"name":"Department of Psychology, City University London, London EC1V 0HB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuel M.","family":"Pothos","sequence":"additional","affiliation":[{"name":"Department of Psychology, City University London, London EC1V 0HB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei","family":"Khrennikov","sequence":"additional","affiliation":[{"name":"International Center for Mathematical Modeling in Physics and Cognitive Sciences Linnaeus University, 351 95 V\u00e4xj\u00f6-Kalmar, Sweden"},{"name":"National Research University of Information Technologies, Mechanics and Optics, St. Petersburg 197101, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,23]]},"reference":[{"key":"ref_1","first-page":"273","article-title":"Thermodynamik quantummechanischer Gesamheiten","volume":"1","year":"1927","journal-title":"Gott. 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