Dynamical Entropy of Quasi-local Algebras

Quantum and Non-Commutative Analysis ◽

10.1007/978-94-017-2823-2_11 ◽

1993 ◽

pp. 149-165

Author(s):

Yong Moon Park

Keyword(s):

Local Algebras ◽

Dynamical Entropy

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Dynamical entropy of quasi-local algebras in quantum statistical mechanics

Communications in Mathematical Physics ◽

10.1007/bf02099194 ◽

1992 ◽

Vol 144 (1) ◽

pp. 149-161 ◽

Cited By ~ 4

Author(s):

Yong Moon Park ◽

Hyun Hye Shin

Keyword(s):

Statistical Mechanics ◽

Quantum Statistical Mechanics ◽

Local Algebras ◽

Dynamical Entropy ◽

Quantum Statistical

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On (n+1)-subwebs of an (n+1)-web and local algebras associated with them

Acta Mathematica Hungarica ◽

10.1007/bf01874218 ◽

1993 ◽

Vol 62 (1-2) ◽

pp. 57-79 ◽

Cited By ~ 3

Author(s):

V. V. Goldberg

Keyword(s):

Local Algebras

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Applications of Local Algebras of Differentiable Manifolds

Journal of Mathematical Sciences ◽

10.1007/s10958-015-2381-x ◽

2015 ◽

Vol 207 (3) ◽

pp. 485-511 ◽

Cited By ~ 2

Author(s):

M. Jukl ◽

L. Juklová ◽

J. Mikeš

Keyword(s):

Differentiable Manifolds ◽

Local Algebras

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On the Relation between Topological Entropy and Restoration Entropy

Entropy ◽

10.3390/e21010007 ◽

2018 ◽

Vol 21 (1) ◽

pp. 7 ◽

Cited By ~ 1

Author(s):

Christoph Kawan

Keyword(s):

Dynamical Systems ◽

State Estimation ◽

Topological Entropy ◽

Robust Estimation ◽

Data Transmission ◽

Communication Constraints ◽

Dynamical Entropy

In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem that demonstrates that for most dynamical systems, restoration entropy strictly exceeds topological entropy. This implies that robust estimation policies in general require a higher rate of data transmission than non-robust ones. The proof of our theorem is quite short, but uses sophisticated tools from the theory of smooth dynamical systems.

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