Result: The Shannon―McMillan theorem for doubly stochastic operators
Title:
The Shannon―McMillan theorem for doubly stochastic operators
Authors:
Source:
Nonlinearity (Bristol. Print). 25(12):3453-3467
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 1/2 p
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Décalage, Shift, Decalaje, Entropie, Entropy, Entropía, Opérateur stochastique, Stochastic operator, Operador estocástico, Physique mathématique, Mathematical physics, Física matemática, Système classique, Classical system, Sistema clásico, Système dynamique, Dynamical system, Sistema dinámico, Trajectoire, Trajectory, Trayectoria, 37XX
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeze Wyspiańskiego 27, 50-370 Wroclaw, Poland
ISSN:
0951-7715
Rights:
Copyright 2014 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26755539
Database:
PASCAL Archive
Further Information
In this paper we introduce and study an information function for doubly stochastic operators. This generalization of the notion, which is well known for classical dynamical systems, follows the earlier results on the entropy of operators by Downarowicz, Frej and Frej. As a main result we prove two versions of the Shannon―McMillan theorem for doubly stochastic operators, using the relations between the entropy of an operator and the entropy of a shift on a space of trajectories.