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State Entropy and Differentiation Phenomenon
Tokuyama Coll, Japan.
City Univ London, UK.
City Univ London, UK.
Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Natl Res Univ Informat Technol Mech & Opt, Russia. (Int Ctr Math Modeling Phys & Cognit Sci)ORCID-id: 0000-0002-9857-0938
2018 (Engelska)Ingår i: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, nr 6, artikel-id 394Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

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.

Ort, förlag, år, upplaga, sidor
MDPI, 2018. Vol. 20, nr 6, artikel-id 394
Nyckelord [en]
density operator, state entropy, von Neumann entropy, quantum measurement, differentiation
Nationell ämneskategori
Matematik
Forskningsämne
Naturvetenskap, Matematik
Identifikatorer
URN: urn:nbn:se:lnu:diva-77406DOI: 10.3390/e20060394ISI: 000436275400003Scopus ID: 2-s2.0-85048703128OAI: oai:DiVA.org:lnu-77406DiVA, id: diva2:1242819
Tillgänglig från: 2018-08-29 Skapad: 2018-08-29 Senast uppdaterad: 2019-08-29Bibliografiskt granskad

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Khrennikov, Andrei

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