Synopses & Reviews
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.
Table of Contents
Preface.
1. Introduction.
2. Summary of Information Theory.
3. Path Entropies of Non Random Functions.
4. Path Entropies of Random Functions and of Non-Random Distributed Functions.
5. Quantum Entropies of Non-Probabilistic Square Matrices.
6. Complex-Valued Fractional Brownian Motion of Order
n Part I.
7. Complex-Valued Fractional Brownian Motion of Order
n. Part II.
8. Information Thermodynamics and Complex-Valued Fractional Brownian motion of Order
n.
9. Fractals, Path, Entropy, and Fractional Fokker-Planck Equation.
10. Outline of Applications. Index.