Mathematical Theory Of Entropy


Mathematical Theory Of Entropy
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Mathematical Theory Of Entropy


Mathematical Theory Of Entropy
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Author : Nathaniel F. G. Martin
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-02

Mathematical Theory Of Entropy written by Nathaniel F. G. Martin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Computers categories.


This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.



Mathematical Theory Of Entropy


Mathematical Theory Of Entropy
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Author : Professor Nathaniel F G Martin
language : en
Publisher:
Release Date : 2014-05-14

Mathematical Theory Of Entropy written by Professor Nathaniel F G Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with categories.


This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.



Mathematical Theory Of Entropy


Mathematical Theory Of Entropy
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Author : N. F. G. Martin
language : en
Publisher:
Release Date :

Mathematical Theory Of Entropy written by N. F. G. Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.




Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications


Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications
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Author : M Zuhair Nashed
language : en
Publisher: World Scientific
Release Date : 2022-08-30

Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications written by M Zuhair Nashed and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-30 with Science categories.


Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational methods, and applications in mathematics, physics, statistics, engineering, biomedical signals, and signal processing.In the last century classical concepts of entropy were introduced in the areas of thermodynamics, information theory, probability theory, statistics, dynamical systems, and ergodic theory. During the past 50 years, dozens of new concepts of entropy have been introduced and studied in many disciplines. This volume captures significant developments in this arena. It features expository, review, and research papers by distinguished mathematicians and scientists from many disciplines. The level of mathematics ranges from intermediate level to research level. Each chapter contains a comprehensive list of references. Topics include entropy and society, entropy and time, Souriau entropy on symplectic model of statistical physics, new definitions of entropy, geometric theory of heat and information, maximum entropy in Bayesian networks, maximum entropy methods, entropy analysis of biomedical signals (review and comparison of methods), spectral entropy and its application to video coding and speech coding, a comprehensive review of 50 years of entropy in dynamics, a comprehensive review on entropy, entropy-like quantities and applications, topological entropy of multimodal maps, entropy production in complex systems, entropy production and convergence to equilibrium, reversibility and irreversibility in entropy, nonequilibrium entropy, index of various entropy, entropy and the greatest blunder ever.



Entropy And Information Theory


Entropy And Information Theory
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Author : Robert M. Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Entropy And Information Theory written by Robert M. Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.


This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.



Mathematical Foundations Of Information Theory


Mathematical Foundations Of Information Theory
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Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1957-01-01

Mathematical Foundations Of Information Theory written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957-01-01 with Mathematics categories.


First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.



Mathematical Theory Of Nonequilibrium Steady States


Mathematical Theory Of Nonequilibrium Steady States
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Author : Da-Quan Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Mathematical Theory Of Nonequilibrium Steady States written by Da-Quan Jiang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Markov processes categories.




Hyperbolic Systems Of Conservation Laws And The Mathematical Theory Of Shock Waves


Hyperbolic Systems Of Conservation Laws And The Mathematical Theory Of Shock Waves
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Author : Peter D. Lax
language : en
Publisher: SIAM
Release Date : 1973-01-01

Hyperbolic Systems Of Conservation Laws And The Mathematical Theory Of Shock Waves written by Peter D. Lax and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-01-01 with Technology & Engineering categories.


This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.



Entropy


Entropy
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Author : Andreas Greven
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08

Entropy written by Andreas Greven and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.


The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.



The Mathematical Theory Of Communication


The Mathematical Theory Of Communication
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Author : Claude E Shannon
language : en
Publisher:
Release Date : 1949

The Mathematical Theory Of Communication written by Claude E Shannon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949 with Computers categories.


Shannon's major precept, that all communication is essentially digital, is commonplace among the digitalia that many wonder why Shannon needed to state such an obvious axiom.