Convexity in the Theory of Lattice Gases

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A01=Robert B. Israel
Abelian von Neumann algebra
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Author_Robert B. Israel
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Banach space
Blaschke selection theorem
Boundary value problem
Bounded set (topological vector space)
Category1=Non-Fiction
Category=PHFC
Characteristic function (probability theory)
Choquet theory
Convex combination
Convex cone
Convex function
Convex hull
Convex set
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Correlation function
Correlation function (quantum field theory)
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Density matrix
Diagram (category theory)
Difference quotient
Differentiable function
Dimension (vector space)
Dirac delta function
Distribution (mathematics)
Enthalpy
eq_isMigrated=2
eq_non-fiction
eq_science
Equation
Expectation value (quantum mechanics)
Extreme point
Ferromagnetism
Hausdorff dimension
Hausdorff measure
Heisenberg model (quantum)
Hyperbolic function
Hölder's inequality
Inclusion–exclusion principle
Inequality (mathematics)
Infimum and supremum
Integral equation
KMS state
Language_English
Laws of thermodynamics
Liouville's theorem (complex analysis)
Mean field theory
Metric space
Morera's theorem
Naturalness (physics)
Non-equilibrium thermodynamics
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Partition function (statistical mechanics)
Phase diagram
Phase rule
Phase space
Phase transition
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Probability measure
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Quantum statistical mechanics
Quantum system
Radon–Nikodym theorem
Riesz representation theorem
Second law of thermodynamics
Set (mathematics)
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Statistical mechanics
Stone–Weierstrass theorem
Subset
Symmetry breaking
Tangent space
Theorem
Theory
Thermodynamic equilibrium
Thermodynamic limit
Thermodynamic system
Thermodynamic temperature
Thermodynamics
Variational inequality
Variational principle
Weak operator topology

Product details

  • ISBN 9780691606194
  • Weight: 340g
  • Dimensions: 152 x 235mm
  • Publication Date: 08 Mar 2015
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Paperback
  • Language: English
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In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.