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Problemy Peredachi Informatsii, 2021, Volume 57, Issue 3, Pages 90–101
DOI: https://doi.org/10.31857/S0555292321030062 (Mi ppi2349) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Large Systems

Geometric interpretation of entropy: new results

G. D. Dvorkin

Department of Mathematical Statistics and Random Processes, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (186 kB) Citations (4)
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DOI: https://doi.org/10.31857/S0555292321030062
Abstract: We consider a relation between the metric entropy and local boundary deformation rate (LBDR) in the symbolic case. We prove that the LBDR understood as a limit in the mean is equal to the entropy for systems containing an essentially synchronized subshift of full measure. We also obtain an example of this relation in the case where such a subshift is lacking. We show for the first time that if the LBDR is understood as a limit almost everywhere, then the equality between this quantity and the entropy need not hold.
Keywords: metric entropy, local boundary deformation rate, symbolic system, synchronized system, invariant ergodic measure, regular bracket sequence, Dyck system.
Received: 25.03.2021
Revised: 17.06.2021
Accepted: 27.06.2021
English version:
Problems of Information Transmission, 2021, Volume 57, Issue 3, Pages 281–291
DOI: https://doi.org/10.1134/S0032946021030066
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 517.938 : 519.722
Language: Russian
Citation: G. D. Dvorkin, “Geometric interpretation of entropy: new results”, Probl. Peredachi Inf., 57:3 (2021), 90–101; Problems Inform. Transmission, 57:3 (2021), 281–291
Citation in format AMSBIB
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\paper Geometric interpretation of entropy: new results
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\pages 90--101
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Проблемы передачи информации Problems of Information Transmission
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    Full-text PDF :4
    References:35
    First page:28
     
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