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Symmetry breakdown in statistical mechanics

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_69_30/P_69_30.pdf

Lecture given at the Ecole d'Eté de Physique Théorique. Cargèse, Corsica, 1969.

Abstract : We discuss the general problem of symmetry beakdown in the algebraic approach to statistical mechanics. We consider in particular the case of classical…

Mots-clés: 1969, ABEL, ALAOGLU, BIRKHOFF, BISHOP, BOREL, CHOQUET, CONGRES ET CONFERENCES, DIXMIER, DOBRUSHIN, EN, EUCLIDE, GIBBS, GINIBRE, HAMILTON, HILBERT, KUBO, LEEUW, MARTIN, MECANIQUE STATISTIQUE, NEUMANN, POWERS, PREPUBLICATION, REYNOLDS, ROBINSON, RUELLE, SCHWINGER, SINAI, SYMETRIE BRISEE, WIGHTMAN

Some Remarks on the ground state of infinite systems in statistical mechanics

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_68_X022/P_68_X022.pdf

Abstract : We investigate the ground states of infinite quantum lattice systems. It is shown in particular that a positive energy operator is associated with these states.

Mots-clés: 1968, ALAOGLU, BAIRE, BANACH, BOURBAKI, EN, HAMILTON, HILBERT, MECANIQUE STATISTIQUE, PREPUBLICATION, RUELLE, VAN HOVE

Statistical mechanics of a one-dimensional lattice gas

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_67_X016/P_67_X016.pdf

Abstract : We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result of Van Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the…

Mots-clés: 1967, ASCOLI, BANACH, EN, GAZ, GIBBS, MECANIQUE STATISTIQUE, PREPUBLICATION, RESEAUX, RUELLE, STEINHAUS, VAN HOVE

Almost periodic states on C-algebras )

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_67_X015/P_67_X015.pdf

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,…

Mots-clés: 1967, ABEL, BOURBAKI, C*-ALGEBRES, EN, GEL'FAND, GROUPES D'AUTOMORSPHISME, HAAR, JACOBS, NEUMANN, PREPUBLICATION, RUELLE

A Variational formulation of equilibrium statistical mechanics and the Gibbs phase rule

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_67_X012/P_67_X012.pdf

Abstract : It is shown that for an infinite lattice system, thermodynamic equilibrium is the solution of a variational problem involving a mean entropy of states introduced earlier [2]. As an application, a version of the Gibbs phase rule is proved.

Mots-clés: 1967, ABEL, BANACH, EN, ENTROPIE, GIBBS, PHYSIQUE STATISTIQUE, PREPUBLICATION, RESEAUX, RUELLE, STONE, SYSTEMES COMPLEXES, WEIERSTRASS

Condensation of lattice gases

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_66_X005/P_66_X005.pdf

Mots-clés: 1966, CONDENSATION, DOBRUSHIN, EN, GAZ, GINIBRE, GRIFFITHS, GROSSMANN, PHYSIQUE STATISTIQUE, PREPUBLICATION, RESEAUX, RUELLE, SYSTEMES COMPLEXES

Mean entropy of States in classical statistical mechanics

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_66_04/P_66_04.pdf

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…

Mots-clés: 1966, ABEL, BILLINGSLEY, EN, ENTROPIE, EUCLIDE, GEL'FAND, JACOBS, KOLMOGOROV, LEBESGUE, MACMILLAN, NIANI, PHYSIQUE STATISTIQUE, PREPUBLICATION, RESEAUX, ROBINSON, ROKHLIN, RUELLE, SYSTEMES COMPLEXES

Integral représentations of invariant states on B*-algebras

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_66_03/P_66_03.pdf

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.,…

Mots-clés: 1966, ABEL, ALAOGLU, ALGEBRES, BIRKHOFF, CHOQUET, EN, GEL'FAND, GROUPES D'AUTOMORPHISMES, INVARIANTS, LANFORD, NAGY, NEUMANN, PREPUBLICATION, RIESZ, RUELLE, SEGAL, STONE, WEIERSTRASS

The States of classical statistical mechanics

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_66_02/P_66_02.pdf

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,…

Mots-clés: 1966, ABEL, EN, FOCK, GEL'FAND, GIBBS, HILBERT, LEBESGUE, MECANIQUE STATISTIQUE, PREPUBLICATION, RUELLE, SEGAL

Extremal invariant states

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_66_01/P_66_01.pdf

Abstract : A number of results are derived which are pertinent to the description of physical systems by states on C*-algebras invariants under a symmetry group. In particular an integral decomposition relevant to the study of lower symmetry is…

Mots-clés: 1966, C*-ALGEBRES, EN, EUCLIDE, FOURIER, GELFAND, INVARIANTS, NAIMARK, PREPUBLICATION, ROBINSON, RUELLE, SEGAL, SYMETRIE

The Stability of many-particle systems

https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/RUELLE/1965-1976/P_65_03/P_65_03.pdf

Abstract : It is shown that a quantal or classical system of N particles of distinct species ?,? = 1, 2, … ? interacting through pair potentials ???(r) are stable, in the sense that the total energy is always bounded below by ?NB, provided ???(r)…

Mots-clés: 1965, BOLTZMANN, BOSE, COULOMB, DIRAC, DOBRUSHIN, EINSTEIN, EN, FERMI, FISHER, FOURIER, HAMILTON, HERMITE, HILBERT, PHYSIQUE, PREPUBLICATION, RUELLE, STABILITE, THEORIE QUANTIQUE, YUKAWA