McMillan type convergence for quantum Gibbs states

DOI10.1007/BF01196636zbMath0834.46049MaRDI QIDQ1345851

Masanori Ohya, Fumio Hiai, Dénes Petz

Publication date: 1 April 1996

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Shannon-McMillan theoremshift invariant measuresGNS spaceexistence of the entropy densityinfinite tensor products of matrix algebrasnon-commutative extension of McMillan's theorem to quantum Gibbs statessubadditivity of the von Neumann entropytranslation-invariant states

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Free probability and free operator algebras (46L54) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Measures of information, entropy (94A17)

Related Items (1)

Gibbs variational formula for thermal equilibrium states in terms of quantum relative entropy density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong limit theorems in non-commutative probability
• A formulation of noncommutative McMillan theorem
• Ergodic theorems for convex sets and operator algebras
• Ergodic theorems for noncommutative dynamical systems
• Gibbs states of a one dimensional quantum lattice
• Positivity of the K-entropy on non-abelian K-flows
• ENTROPY DENSITIES FOR GIBBS STATES OF QUANTUM SPIN SYSTEMS
• On entropy and information gain in random fields

This page was built for publication: McMillan type convergence for quantum Gibbs states