Integral representation of states on a C*-algebras
RESEAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
SYSTEMES DYNAMIQUES
Abstract : Let E be the compact set of states on a C?-algebra U with identity. We discuss the representations of a state ? as barycenter of a probability measure ? on E. Examples of such representations are the central decomposition and the ergodic decomposition. They are associated with an Abelian von Neumann algebra B in the commutant ?(U)? of the image of U in the representation canonically associated with ?. This situation is studied in general and a number of applications are discussed.
RUELLE
P/70/X029
IHES
1970
A4
30 f.
EN
TEXTE
PREPUBLICATION
P_70_X029.pdf
1970
Almost periodic states on C*-algebras *)
C*-ALGEBRES
GROUPES D'AUTOMORSPHISME
Abstract : Given a C*-algebra O with a group of automorphisms, we define and study almost periodic states on O. A natural decomposition of such states is introduced and discussed.
*) These notes are a result of discussions between S. Dpolicher, G. Gallavotti and D. Ruelle, they are not intended for publication.
RUELLE
P/67/X015
IHES
1967
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_67_X015.pdf
1967
Mean entropy of States in classical statistical mechanics
ENTROPIE
RESEAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
Abstract : The equilibrium states for an infinite system of classical mechanics may be represented by states over Abelian C* algebras. We consider here continuous and lattice systems and define a mean entropy for their states. The properties of this mean entropy are investigated : linearity, upper semi-continuity, integral representations. In the lattice case, it is found that our mean entropy coincides with the KOLMOGOROV-SINAI invariant of ergodic theory.
RUELLE
ROBINSON
P/66/04
IHES
1966
A4
25 f.
EN
TEXTE
PREPUBLICATION
P_66_04.pdf
1966
Integral représentations of invariant states on B*-algebras
INVARIANTS
ALGEBRES
GROUPES D'AUTOMORPHISMES
Abstract : Let ?? be a B* algebra with a group G of automorphisms and K be the set of G?invariant states on ??. We discuss conditions under which a G?invariant state has a unique integral representation in terms of extremal points of K, i.e., extremal invariant states.
RUELLE
LANFORD
P/66/03
IHES
1966
A4
11 f.
EN
TEXTE
PREPUBLICATION
P_66_03.pdf
1966
The States of classical statistical mechanics
MECANIQUE STATISTIQUE
Abstract : a state of an infinite system in classical statistical mechanics is usually described by its correlation functions. We discuss here other description in particular as 1) a state on a B*-algebras, 2) a collection of density distributions, 3) a field theory 4) a mesure on a space of configurations of infitely many particles. We consier the relations between these various descriptions and prove under very general conditions an integral representation of a state as superposition of extremal invariant states corresponding to pure thermodynamical phases.
RUELLE
P/66/02
IHES
1966
A4
31 f.
EN
TEXTE
PREPUBLICATION
P_66_02.pdf
1966