This article is cited in 2 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

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.

UDC: 621.391 : 517.938 : 519.722

Received: 25.03.2021
Revised: 17.06.2021
Accepted: 27.06.2021

DOI: 10.31857/S0555292321030062

 English version: Problems of Information Transmission, 2021, 57:3, 281–291

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