2 00 8 KMS States , Entropy and a Variational Principle for Pressure
نویسنده
چکیده
We want to relate the concepts of entropy and pressure to that of KMS states for C∗-Algebras. Several different definitions of entropy are known in our days. The one we describe here is quite natural and extends the usual one for Dynamical Systems in Thermodynamic Formalism Theory. It has the advantage of been very easy to be introduced. It is basically obtained from transfer operators (also called Ruelle operators). Later we introduce the concept of pressure as a min-max principle. Finally, we consider the concept of a KMS state as an equilibrium state for a potential (in the context of C∗-Algebras) and we show that there is a relation between KMS states for certain algebras coming from a continuous transformation and equilibrium measures. ∗Instituto de Matemática, UFRGS, 91509-900 Porto Alegre, Brasil. Partially supported by CNPq, PRONEX – Sistemas Dinâmicos, Instituto do Milênio, and beneficiary of CAPES financial support.
منابع مشابه
. O A ] 1 8 D ec 1 99 9 KMS STATES , ENTROPY AND THE VARIATIONAL PRINCIPLE IN FULL C ∗ – DYNAMICAL SYSTEMS
To any periodic and full C∗–dynamical system (A, α,R) a certain invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron–Frobenius theorem asserts the existence of KMS states at inverse temperatures the logarithm of the inner and outer spectral radii of s. Such KMS st...
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To any periodic and full C∗–dynamical system (A, α,R), an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron–Frobenius type theorem asserts the existence of KMS states at inverse temperatures equal the logarithms of the inner and outer spectral radii of s (extre...
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