Asymptotic of Varadhan-type and the Gibbs variational principle
type: Item
instance of: scholarly article
title: Asymptotic of Varadhan-type and the Gibbs variational principle
zbMATH Open document ID: 0682.46054
DOI: 10.1007/BF01217806
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The authors deal with the following: For a large class of quantum models of meanfield type the thermodynamic limit of the free energy density is proved to be given by the Gibbs variational principle. The latter is exhibited to be equivalent to a non-commutative version of Varadhan's asymptotic formula.
reviewed by: Seshadri Sridhar
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 4117255
zbMATH Keywords: quantum models of meanfield type
zbMATH Keywords: thermodynamic limit of the free energy density
zbMATH Keywords: Gibbs variational principle
zbMATH Keywords: non-commutative version of Varadhan's asymptotic formula
author: Dénes Petz
author: G. A. Raggio
author: A. Verbeure
MaRDI profile type: Publication
cites work: Relative Hamiltonian for faithful normal states of a von Neumann algebra
cites work: Golden-Thompson and Peierls-Bogolubov inequalities for a general von Neumann algebra
cites work: On uniqueness of KmMS states of one-dimensional quantum lattice systems
cites work: Relative entropy for states of von Neumann algebras. II
cites work: Positive cones and \(L^p\)-spaces for von Neumann algebras
cites work: Q3913911
cites work: The free energy of quantum spin systems and large deviations
cites work: Q3681702
cites work: Equilibrium states for mean field models
cites work: Quasi-entropies for finite quantum systems
cites work: A variational expression for the relative entropy
cites work: Q5508589
cites work: Q4150490
cites work: Symmetric states of infinite tensor products of \(C^ *\)-algebras
cites work: Q3876492
cites work: Conditional expectation in an operator algebra. IV. Entropy and information
cites work: Asymptotic probabilities and differential equations
cites work: Q3341599
full work available at URL: https://doi.org/10.1007/bf01217806
OpenAlex ID: W2023795213
description: scientific article; zbMATH DE number 4117255