Displaying similar documents to “The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups”

On the directional entropy for ℤ²-actions on a Lebesgue space

B. Kamiński, K. Park (1999)

Studia Mathematica

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We define the concept of directional entropy for arbitrary ℤ 2 -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.

On the entropy for group actions on the circle

Eduardo Jorquera (2009)

Fundamenta Mathematicae

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We show that for a finitely generated group of C² circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.

Wehrl entropy of the state in a two-atom Tavis-Cummings model

Debraj Nath, P. K. Das (2011)

Banach Center Publications

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In this paper we present an entropic description of quantum state obtained by interaction of one mode of quantized electromagnetic field with two two-level atoms inside a cavity, known as Tavis-Cumming model. Wehrl entropy has been calculated analytically and investigated as a function of the average value of the photon number operator. Husimi's Q function has been calculated and compared with the behaviour of the field entropy.

Complete positivity of entropy and non-Bernoullicity for transformation groups

Valentin Golodets, Sergey Sinel'shchikov (2000)

Colloquium Mathematicae

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The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.

Abelian groups of zero adjoint entropy

L. Salce, P. Zanardo (2010)

Colloquium Mathematicae

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The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of...

Metric Entropy of Nonautonomous Dynamical Systems

Christoph Kawan (2014)

Nonautonomous Dynamical Systems

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We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn, μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the...