Non-cooperative equilibria of Fermi systems with long range interactions / / J.-B. Bru, W. de Siqueira Pedra

• Record Nr.: UNINA9910828121603321
• Autore: Bru J.-B (Jean-Bernard), <1973->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• ISBN: 1-4704-1003-6
• Descrizione fisica: 1 online resource (155 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 224, Number 1052
• Disciplina: 530.155732
• Soggetti: Thermodynamic equilibrium; Phase rule and equilibrium; Mathematical models; Nuclear spin; Long range order (Solid state physics)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 224, Number 1052 (first of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: ""Contents""; ""Preface""; ""Part 1 . Main Results and Discussions""; ""Chapter 1. Fermi Systems on Lattices""; ""1.1. Local fermion algebras""; ""1.2. States of Fermi systems on lattices""; ""1.3. The spaceâ€?averaging functional Î?_{ }""; ""1.4. Local interactions and internal energies""; ""1.5. Energy and entropy densities""; ""Chapter 2. Fermi Systems with Longâ€?Range Interactions""; ""2.1. Fermi systems with longâ€?range interactions""; ""2.2. Examples of applications""; ""2.3. Freeâ€?energy densities and existence of thermodynamics""; ""2.4. Generalized t.i. equilibrium states""; ""2.5. Structure of the set \varOmega_{ }^{â?}̄ of generalized t.i. equilibrium states""""2.6. Gibbs states versus generalized equilibrium states""; ""2.7. Thermodynamics and game theory""; ""2.8. Gap equations and effective theories""; ""2.9. Longâ€?range interactions and longâ€?range order (LRO)""; ""2.10. Concluding remarks""; ""Part 2 . Complementary Results""; ""Chapter 3. Periodic Boundary Conditions and Gibbs Equilibrium States""; ""3.1. Interaction kernels""; ""3.2. Periodic boundary conditions""; ""3.3. Pressure and periodic boundary ; conditions""; ""3.4. Gibbs and generalized t.i. equilibrium states""""Chapter 4. The Set _{â??â??} of â??â??.â??^{ }â€?Invariant States""; ""4.1. GNS representation and the von Neumann ergodic theorem""; ""4.2. The set â?°_{â??â??} of extreme states of â?°_{â??â??}""; ""4.3. Properties of the spaceâ€?averaging functional Î?_{ }""; ""4.4. Von Neumann entropy and entropy density of â??â??â€?periodic states""; ""4.5. The set â?? as a subset of the dual space â??*""; ""4.6. Wellâ€?definiteness of the freeâ€?energy densities on _{â??â??}""; ""Chapter 5. Permutation Invariant Fermi Systems""; ""10.6. The Legendreâ€?Fenchel transform and tangent functionals""