Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach: 112 (Fundamental Theories of Physics, 112) - Tapa dura

Jumarie, Guy

 
9780792363309: Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach: 112 (Fundamental Theories of Physics, 112)
Tapa dura
ISBN 10: 0792363302 ISBN 13: 9780792363309
Editorial: Springer, 2000

Sinopsis

Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon’s information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon’s information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon’s theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.

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Reseña del editor

Every thought is a throw of dice. Stephane Mallarme This book is the last one of a trilogy which reports a part of our research work over nearly thirty years (we discard our non-conventional results in automatic control theory and applications on the one hand, and fuzzy sets on the other), and its main key words are Information Theory, Entropy, Maximum Entropy Principle, Linguistics, Thermodynamics, Quantum Mechanics, Fractals, Fractional Brownian Motion, Stochastic Differential Equations of Order n, Stochastic Optimal Control, Computer Vision. Our obsession has been always the same: Shannon's information theory should play a basic role in the foundations of sciences, but subject to the condition that it be suitably generalized to allow us to deal with problems which are not necessarily related to communication engineering. With this objective in mind, two questions are of utmost importance: (i) How can we introduce meaning or significance of information in Shannon's information theory? (ii) How can we define and/or measure the amount of information involved in a form or a pattern without using a probabilistic scheme? It is obligatory to find suitable answers to these problems if we want to apply Shannon's theory to science with some chance of success. For instance, its use in biology has been very disappointing, for the very reason that the meaning of information is there of basic importance, and is not involved in this approach.

Reseña del editor

This book presents material on three topics, namely the amount of information involved in non-random functions, the amount of information involved in non-probabilistic square matrices (i.e. which are not quantum density matrices), and a new model of complex-valued fractional Brownian motion of order n defined via random walks in the complex plane. These three subjects, which on the surface have no common features, are, in fact, direct consequences of the maximum entropy principle. Moreover, information on non-random functions and complex fractional Brownian motion are directly related to fractals. Thus, a unified framework is constructed which encompasses information with and without probability, quantum information of square matrices with and without probabilistic meaning, and fractals in the complex plane. This volume also features many applications.
Audience: This work is intended for theoretical and mathematical physicists, but also for applied mathematicians, experimental physicists, communication engineers, electrical engineers, practitioners in pattern recognition and computer vision, control systems engineers, and theoretical biologists.

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Editorial
Springer
Año de publicación
2000
Idioma
Inglés
ISBN 10 
0792363302
ISBN 13 
9780792363309
Encuadernación
Tapa dura
Número de páginas
296
Contacto del fabricante
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Darmstadt
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Alemania

Otras ediciones populares con el mismo título

9789048154678: Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach: 112 (Fundamental Theories of Physics)

Edición Destacada

ISBN 10:  9048154677 ISBN 13:  9789048154678
Editorial: Springer, 2010
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