FRONTIERS IN ENTROPY ACROSS THE DISCIPLINES

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. Contents: Entropy and Society: Can the Physical/Mathematical Notions of Entropy Be Usefully Imported into the Social Sphere? (Philip J Davis) Entropy and Time (Olimpia Lombardi and Cristian López) Souriau Entropy Based on Symplectic Model of Statistical Physics Three Jean-Marie Souriau's Seminal Papers on Lie Groups Thermodynamics (Frédéric Barbaresco) A New Definition of Entropy Based on Shannon's Measure of Information (Arieh Ben-Naim) Entropy Geometric Structure as Casimir Invariant Function in Coadjoint Representation: Geometric Theory of Heat & Information Based on Souriau Lie Groups Thermodynamics and Lie Algebra Cohomology (Frédéric Barbaresco) The Maximum Entropy Formalism and Its Utilization in Bayesian Networks (Dawn E Holmes) Maximum Entropy Methods (Jiu Ding) On Entropy, Entropy-like Quantities, and Applications (José M Amigó, Karsten Keller and Valentina A Unakafova) Entropy Analysis of Univariate Biomedical Signals Review and Comparison of Methods (Hamed Azami, Luca Faes, Javier Escudero, Anne Humeau-Heurtier and Luiz E V Silva) Spectral Entropy Coefficient Rate, Equivalent Bandwidth, Theoretical Dimension, and Effective Rank (Jerry Gibson, Wenye Yang and Jaewoo Jung) Video Coding Using the Spectral Entropy Method (Jaewoo Jung and Jerry Gibson) Spectral Entropy Wideband Speech Coding (Mark G Kokes and Jerry D Gibson) Fifty Years of Entropy in Dynamics: 1958–2007 (Anatoloe Katok) Combining Lower Bounds on Entropy Production in Complex Systems with Multiple Interacting Components (David H Wolpert) Entropy Production and Convergence to Equilibrium (Cédric Villani) (Ir)reversibility and Entropy (Cédric Villani) Convergence to Equilibrium: Entropy Production and Hypocoercivity (Cédric Villani) Non-equilibrium Entropy in an Extended State Space (P D Gujrati) Index of Various Entropies (Takuya Yamano) A Simplified Algorithm for the Topological Entropy of Multimodal Maps (José M Amigó and Ángel Giménez) Entropy, the Greatest Blunder Ever (Arieh Ben-Naim) Readership: Physicists, Mathematicians, Engineers, and Biomedical Researchers. Key Features: Most comprehensive collection of chapters in one volume Covers theory, computation, and applications of entropy across many disciplines