On the equivalence of the KMS condition and the variational principle for quantum lattice systems
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Publication:1847028
DOI10.1007/BF01651545zbMath0289.46048OpenAlexW1523989160MaRDI QIDQ1847028
Publication date: 1974
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01651545
General theory of von Neumann algebras (46L10) Information theory (general) (94A15) Ordered topological linear spaces, vector lattices (46A40) Ideals and subalgebras (46H10)
Related Items (20)
On the relative entropy ⋮ Strong Martingale Convergence of Generalized Conditional Expectations on Von Neumann Algebras ⋮ Operator algebras in statistical mechanics and noncommutative probability theory ⋮ Large deviations in weakly interacting fermions: Generating functions as Gaussian Berezin integrals and bounds on large Pfaffians ⋮ EQUILIBRIUM STATES AND THEIR ENTROPY DENSITIES IN GAUGE-INVARIANT C*-SYSTEMS ⋮ VARIATIONAL PRINCIPLE FOR NON-EQUILIBRIUM STEADY STATES OF THE XX MODEL ⋮ Gibbs variational formula for thermal equilibrium states in terms of quantum relative entropy density ⋮ QUANTUM MECHANICS IN AFC*-SYSTEMS ⋮ Thermalization and canonical typicality in translation-invariant quantum lattice systems ⋮ RUELLE–LANFORD FUNCTIONS AND LARGE DEVIATIONS FOR ASYMPTOTICALLY DECOUPLED QUANTUM SYSTEMS ⋮ EQUILIBRIUM STATISTICAL MECHANICS OF FERMION LATTICE SYSTEMS ⋮ On uniqueness of KmMS states of one-dimensional quantum lattice systems ⋮ Equilibrium states of a semi-quantum lattice system ⋮ The pure phases (harmonic functions) of generalized processes or: Mathematical physics of phase transitions and symmetry breaking ⋮ Ground states of quantum spin systems ⋮ The cluster expansion for classical and quantum lattice systems ⋮ Large deviations in quantum lattice systems: one-phase region ⋮ Some contact points of mathematics and physics ⋮ Martingale-type convergence of modular automorphism groups on von Neumann algebras ⋮ Entropy transmission in \(C^*\)-dynamical systems
Cites Work
- Expectations and entropy inequalities for finite quantum systems
- Relative Hamiltonian for faithful normal states of a von Neumann algebra
- Golden-Thompson and Peierls-Bogolubov inequalities for a general von Neumann algebra
- Statistica mechanics of quantum spin systems. III
- Normal positive linear mappings of norm 1 from a von Neumann algebra into its commutant and its application
- Conditional expectation in an operator algebra. IV. Entropy and information
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