Entropy at a weight-per-symbol and embeddings of Markov chains.
Brian Marcus, Selim Tuncel (1990)
Inventiones mathematicae
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Brian Marcus, Selim Tuncel (1990)
Inventiones mathematicae
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Dénes Petz (1991)
Mathematische Zeitschrift
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Gabrielli, D., Galves, A., Guiol, D. (2003)
Mathematical Physics Electronic Journal [electronic only]
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Tim Austin (2015)
Studia Mathematica
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A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties. On the other hand, Makarov has shown that this...
R. F. Streater (2004)
Banach Center Publications
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We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas. We show that the system does not produce entropy.
Boyarsky, Abraham, Góra, Paweł (2000)
Discrete Dynamics in Nature and Society
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Bartosz Frej (2006)
Fundamenta Mathematicae
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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.
Lino G. Marujo, Raad Y. Qassim (2014)
RAIRO - Operations Research - Recherche Opérationnelle
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This work aims to fill a lacunae in the project-oriented production systems literature providing a formal analytic description of the rework effects formulae and the determination of the extended design time due to a certain degree of overlapping in a pair of activities. It is made through the utilization of concepts of workflow construction with hidden (semi) Markov models theory and establishing a way to disaggregate activities into sub-activities, in order to determine the activity...
Mike Boyle, Jérôme Buzzi, Ricardo Gómez (2014)
Colloquium Mathematicae
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We show that strongly positively recurrent Markov shifts (including shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Bartosz Frej, Paulina Frej (2011)
Fundamenta Mathematicae
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A new formula for entropy of doubly stochastic operators is presented. It is also checked that this formula fulfills the axioms of the axiomatic definition of operator entropy, introduced in an earlier paper of Downarowicz and Frej. As an application of the formula the 'product rule' is obtained, i.e. it is shown that the entropy of a product is the sum of the entropies of the factors. Finally, the proof of continuity of the new 'static' entropy as a function of the measure is given. ...
Wolfgang Krieger, Joachim Cantz (1980)
Journal für die reine und angewandte Mathematik
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Chakrabarti, C.G., De, Kajal (2000)
International Journal of Mathematics and Mathematical Sciences
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Christian Mauduit, Carlos Gustavo Moreira (2010)
Acta Arithmetica
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Manfred Denker, Hajo Holzmann (2008)
Colloquium Mathematicae
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Fibre expanding systems have been introduced by Denker and Gordin. Here we show the existence of a finite partition for such systems which is fibrewise a Markov partition. Such partitions have direct applications to the Abramov-Rokhlin formula for relative entropy and certain polynomial endomorphisms of ℂ².
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.
Chakrabarti, C.G., Chakrabarty, Indranil (2005)
International Journal of Mathematics and Mathematical Sciences
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