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

Ruelie, David

doi:10.1090/S0002-9947-1973-0417391-6

Statistical mechanics on a compact set with $Z^{v}$ action satisfying expansiveness and specification
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Trans. Amer. Math. Soc. 185 (1973), 237-251 Request permission

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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