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.

This book focuses on analysing the applications of the Shannon Measure of Information (SMI). The book introduces the concept of frustration and discusses the question of the quantification of this concept within information theory (IT), while it also focuses on the interpretation of the entropy of systems of interacting particles in terms of the SMI and of mutual information. The author examines the question of the possibility of measuring the extent of frustration using mutual information and discusses some classical examples of processes of mixing and assimilation for which the entropy changes are interpreted in terms of SMI. A description of a few binding systems and the interpretation of cooperativity phenomena in terms of mutual information are also presented, along with a detailed discussion on the general method of using maximum SMI in order to find the “best-guess” probability distribution. This book is a valuable contribution to the field of information theory and will be of great interest to any scientist who is interested in IT and in its potential applications.

Have you read or are you planning to read any of the following books? 1: "A Brief History of Time," by S. Hawking (1988)2: "A Briefer History of Time," by S. Hawking and L. Mlodinow (2005)3: "Decoding the Universe," by C. Seife (2007)4: "Programming the Universe," by S. Lloyd (2006)5: "From Eternity to Here," by S. Carroll (2010)6: "The Big Picture: On the Origins of Life, Meaning and the Universe itself," by S. Carroll (2016)7: "Now, The Physics of Time," by R. Muller (2016)8: "The Order Time," by C. Rovelli (2018)Then this book is for you!What drives the popular science book industry today? Do marketing and profit lead the way? Or do honesty and first principle thinking still hold as its core value? This book argues for maintaining the latter and takes a critical look at eight "best-selling" popular science books which spread erroneous ideas and misinformation on topics such as Time, Entropy, Information Theory, and the Second Law of Thermodynamics. Using humor and reason the author puts under the microscope and scrutinizes the confusion and ignorance spread by some of popular sciences' greatest authors. It is written in simple, clear language which is accessible to scientists as well as to laypersons. The author, Arieh Ben-Naim, is a professor emeritus of the Department of Physical Chemistry of the Hebrew University in Jerusalem, Israel. He has published over twenty books and most of his research work focused on the theory of liquids and solutions and understanding the peculiar and outstanding properties of water and the role of water in biological systems. In recent years, the author shifted his focus toward clarifying and explaining to the wider public audience one of the most mysterious concepts in Physics: Entropy. Deemed by numerous scientists as a concept that will forever remain shrouded in mystery, the author set out on a mission to demystify the concept of entropy and provide a platform to hold popular science writing accountable to the highest level for both the lay and advanced reader alike.

Why do we exist? For centuries, this question was the sole province of religion and philosophy. But now science is ready to take a seat at the table. According to the prevailing scientific paradigm, the universe tends toward randomness; it functions according to laws without purpose, and the emergence of life is an accident devoid of meaning. But this bleak interpretation of nature is currently being challenged by cutting-edge findings at the intersection of physics, biology, neuroscience, and information theory—generally referred to as “complexity science.” Thanks to a new understanding of evolution, as well as recent advances in our understanding of the phenomenon known as emergence, a new cosmic narrative is taking shape: Nature’s simplest “parts” come together to form ever-greater “wholes” in a process that has no end in sight. In The Romance of Reality, cognitive neuroscientist Bobby Azarian explains the science behind this new view of reality and explores what it means for all of us. In engaging, accessible prose, Azarian outlines the fundamental misunderstanding of thermodynamics at the heart of the old assumptions about the universe’s evolution, and shows us the evidence that suggests that the universe is a “self-organizing” system, one that is moving toward increasing complexity and awareness. Cosmologist and science communicator Carl Sagan once said of humanity that “we are a way for the cosmos to know itself.” The Romance of Reality shows that this poetic statement in fact rests on a scientific foundation and gives us a new way to know the cosmos, along with a riveting vision of life that imbues existence with meaning—nothing supernatural required.

"An accessible and engaging exploration of the mysteries of time." -Brian Greene, author of The Elegant Universe Twenty years ago, Stephen Hawking tried to explain time by understanding the Big Bang. Now, Sean Carroll says we need to be more ambitious. One of the leading theoretical physicists of his generation, Carroll delivers a dazzling and paradigm-shifting theory of time's arrow that embraces subjects from entropy to quantum mechanics to time travel to information theory and the meaning of life. From Eternity to Here is no less than the next step toward understanding how we came to exist, and a fantastically approachable read that will appeal to a broad audience of armchair physicists, and anyone who ponders the nature of our world.

The aim of this book is to explain in simple language what we know and what we do not know about information and entropy -- two of the most frequently discussed topics in recent literature -- and whether they are relevant to life and the entire universe. Entropy is commonly interpreted as a measure of disorder. This interpretation has caused a great amount of "disorder" in the literature. One of the aims of this book is to put some "order" in this "disorder." The book explains with minimum amount of mathematics what information theory is and how it is related to thermodynamic entropy. Then it critically examines the application of these concepts to the question of "What is life?" and whether or not they can be applied to the entire universe.

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