Journal ArticleDOI
Generalized $K$-flows
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In this article, the classical concept of K-flow is generalized to cover situations encountered in non-equilibrium quantum statistical mechanics and the ergodic properties of generalized K-flows are discussed.Abstract:
The classical concept of K-flow is generalized to cover situations encountered in non-equilibrium quantum statistical mechanics The ergodic properties of generalized K-flows are discussed Several non-isomorphic examples are constructed, which differ already in the type (II1, III),, and III1) of the factor on which they are defined In particular, generalized factor K-flows with dynamical entropy either zero (singular K-flows) or infinite (special non-abelian K-flows) are constructedread more
Citations
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General properties of entropy
TL;DR: This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.
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Markov dilations on W∗-algebras
TL;DR: In this paper, a systematic study of Markov dilations for completely positive operators on W ∗ -algebras which leave a faithful normal state invariant was carried out and it was shown that a minimal Markov dilation preserves important properties of the underlying completely positive operator.
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Non-Markovian quantum stochastic processes and their entropy
TL;DR: In this paper, a quantum stochastic process (QSP) in discrete time capable of describing non-Markovian effects is introduced, which is based directly on the physically relevant correlation functions.
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Frobenius Theory for Positive Maps of von Neumann Algebras
TL;DR: In this article, Frobenius theory about the cyclic structure of eigenvalues of irreducible nonnegative matrices is extended to the case of positive linear maps of von Neumann algebras.
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Dirichlet forms and Markov semigroups on $C^*$-algebras
TL;DR: In this article, the authors extend the classical theory of Dirichlet forms and associated Markov semigroups to the case of a C *-algebra with a trace.
References
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Journal ArticleDOI
On the equilibrium states in quantum statistical mechanics
TL;DR: In this article, the authors studied the representation of the C*-algebra of observables corresponding to thermal equilibrium of a system at given temperature T and chemical potential μ and showed that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of\(\mathfrak{A}\) onto its commutant.
Book
Algebraic methods in statistical mechanics and quantum field theory
TL;DR: In this paper, algebraic methods in statistical mechanics and quantum field theory are presented for finding knowledge and lessons everywhere, but it will involve you to get what call as the preferred thing.