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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Statistical mechanics on a compact set with $ Z^{v}$ action satisfying expansiveness and specification


Author: David Ruelie
Journal: Trans. Amer. Math. Soc. 185 (1973), 237-251
MSC: Primary 28A65; Secondary 82.28, 58F99, 54H20
MathSciNet review: 0417391
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Abstract: We consider a compact set $ \Omega $ with a homeomorphism (or more generally a $ {{\mathbf{Z}}^\nu }$ action) such that expansiveness and Bowen's specification condition hold. The entropy is a function on invariant probability measures. The pressure (a concept borrowed from statistical mechanics) is defined as function on $ \mathcal{C}(\Omega )$--the real continuous functions on $ \Omega $. The entropy and pressure are shown to be dual in a certain sense, and this duality is investigated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0417391-6
PII: S 0002-9947(1973)0417391-6
Article copyright: © Copyright 1973 American Mathematical Society