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Maximizing measures of generic Holder functions have zero entropy
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Morris, Ian D. (2008) Maximizing measures of generic Holder functions have zero entropy. Nonlinearity, Vol.21 (No.5). pp. 993-1000. doi:10.1088/0951-7715/21/5/005 ISSN 0951-7715.
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Official URL: http://dx.doi.org/10.1088/0951-7715/21/5/005
Abstract
We prove that for a generic real-valued Holder continuous function f on a subshift of finite type, every shift-invariant probability measure that maximizes the integral of f must have zero entropy. An immediate corollary is that zero-temperature limits of equilibrium states of certain one-dimensional lattice systems generically have zero entropy. We prove an analogous statement for generic Lipschitz observations of expanding maps of the circle.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Functions, Functions, Continuous, Entropy, Maximum entropy method, Probability measures | ||||
| Journal or Publication Title: | Nonlinearity | ||||
| Publisher: | IOP | ||||
| ISSN: | 0951-7715 | ||||
| Official Date: | May 2008 | ||||
| Dates: |
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| Volume: | Vol.21 | ||||
| Number: | No.5 | ||||
| Number of Pages: | 8 | ||||
| Page Range: | pp. 993-1000 | ||||
| DOI: | 10.1088/0951-7715/21/5/005 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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