Thermodynamic formalism : the mathematical structures of equilibrium statistical mechanics /

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ruelle, David
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2004.
Edición:2nd ed.
Colección:Cambridge mathematical library.
Temas:
Statistical mechanics.
Lattice theory.
Thermodynamics.
Thermodynamics
Mécanique statistique.
Théorie des treillis.
Thermodynamique.
thermodynamics.
SCIENCE > Physics > General.
Lattice theory
Statistical mechanics
Statistische mechanica.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-Title
  • Series-title
  • Title
  • Copyright
  • Dedication
  • Contents
  • Foreword to the first edition
  • Preface to the first edition
  • Preface to the second edition
  • References
  • Introduction
  • 0.1 Generalities
  • 0.2 Description of the thermodynamic formalism
  • I. Finite systems
  • II. Thermodynamic formalism on a metrizable compact set
  • III. Statistical mechanics on a lattice
  • 0.3 Summary of contents
  • 1 Theory of Gibbs states
  • 1.1 Configuration space
  • 1.2 Interactions
  • 1.3 Gibbs ensembles and thermodynamic limit
  • 1.4 Proposition
  • 1.5 Gibbs states.
  • 1.6 Thermodynamic limit of Gibbs ensembles
  • 1.7 Boundary terms
  • 1.8 Theorem
  • 1.9 Theorem
  • 1.10 Algebra at infinity
  • 1.11 Theorem (characterization of pure Gibbs states)
  • 1.12 The operators
  • 1.13 Theorem (characterization of unique Gibbs states)
  • 1.14 Remark
  • Notes
  • Exercises
  • 2 Gibbs states: complements
  • 2.1 Morphisms of lattice systems
  • 2.2 Example
  • 2.3 The interaction F Phi
  • 2.4 Lemma
  • 2.5 Proposition
  • 2.6 Remarks
  • 2.7 Systems of conditional probabilities
  • 2.8 Properties of Gibbs states
  • 2.9 Remark
  • Notes
  • Exercises.
  • 3 Translation invariance. Theory ofequilibrium states
  • 3.1 Translation invariance
  • 3.2 The function APhi
  • 3.3 Partition functions
  • 3.4 Theorem
  • 3.5 Invariant states
  • 3.6 Proposition
  • 3.7 Theorem
  • 3.8 Entropy
  • 3.9 Infinite limit in the sense of van Hove
  • 3.10 Theorem
  • 3.11 Lemma
  • 3.12 Theorem
  • 3.13 Corollary
  • 3.14 Corollary
  • 3.15 Physical interpretation
  • 3.16 Theorem
  • 3.17 Corollary
  • 3.18 Approximation of invariant states by equilibrium states
  • 3.19 Lemma
  • 3.20 Theorem
  • 3.21 Coexistence of phases
  • Notes
  • Exercises.
  • 4 Connection between Gibbs statesand Equilibrium states
  • 4.1 Generalities
  • 4.2 Theorem
  • 4.3 Physical interpretation
  • 4.4 Proposition
  • 4.5 Remark
  • 4.6 Strict convexity of the pressure
  • 4.7 Proposition
  • 4.8 Z-lattice systems and Z-morphisms
  • 4.9 Proposition
  • 4.10 Corollary
  • 4.11 Remark
  • 4.12 Proposition
  • 4.13 Restriction of Z to a subgroup G
  • 4.14 Proposition
  • 4.15 Undecidability and non-periodicity
  • Notes
  • Exercises
  • 5 One-dimensional systems
  • 5.1 Lemma
  • 5.2 Theorem
  • 5.3 Theorem
  • 5.4 Lemma
  • 5.5 Proof of theorems 5.2 and 5.3.
  • 5.6 Corollaries to theorems 5.2 and 5.3
  • 5.7 Theorem
  • 5.8 Mixing Z-lattice systems
  • 5.9 Lemma
  • 5.10 Theorem
  • 5.11 The transfer matrix and the operator
  • 5.12 The function Psi>
  • 5.13 Proposition
  • 5.14 The operator
  • 5.15 Lemma
  • 5.16 Proposition
  • 5.17 Remark
  • 5.18 Exponentially decreasing interactions
  • 5.19 The space and related spaces
  • 5.20 Proposition
  • 5.21 Theorem
  • 5.22 Remarks
  • 5.23 Lemma
  • 5.24 Proposition
  • 5.25 Remark
  • 5.26 Theorem
  • 5.27 Corollary
  • 5.28 Zeta functions
  • 5.29 Theorem
  • Notes
  • Exercises
  • 6 Extension of the thermodynamic formalism.

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