Variational principles of metric mean dimension for random dynamical systems Article Swipe
Yunping Wang
,
Ercai Chen
,
Kexiang Yang
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.16461
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.16461
It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was introduced to characterize infinite fiber entropy systems. We give four types of measure-theoretic $ε$-entropies, called measure-theoretic entropy of partitions decreasing in diameter, Shapira's entropy, Katok's entropy and Brin-Katok local entropy, and establish four variational principles for metric mean dimension.
Related Topics
Concepts
Mathematics
Entropy (arrow of time)
Joint quantum entropy
Fisher information metric
Topological entropy
Maximum entropy probability distribution
Variational principle
Differential entropy
Statistical physics
Mathematical analysis
Pure mathematics
Metric space
Principle of maximum entropy
Injective metric space
Statistics
Physics
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2310.16461
- https://arxiv.org/pdf/2310.16461
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4387963865
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4387963865Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2310.16461Digital Object Identifier
- Title
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Variational principles of metric mean dimension for random dynamical systemsWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-10-25Full publication date if available
- Authors
-
Yunping Wang, Ercai Chen, Kexiang YangList of authors in order
- Landing page
-
https://arxiv.org/abs/2310.16461Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2310.16461Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2310.16461Direct OA link when available
- Concepts
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Mathematics, Entropy (arrow of time), Joint quantum entropy, Fisher information metric, Topological entropy, Maximum entropy probability distribution, Variational principle, Differential entropy, Statistical physics, Mathematical analysis, Pure mathematics, Metric space, Principle of maximum entropy, Injective metric space, Statistics, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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