Download or read book Approaches to Entropy written by Jeremy R. H. Tame and published by Springer. This book was released on 2018-08-30 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about thermodynamics, not history, but it adopts a semi-historical approach in order to highlight different approaches to entropy. The book does not follow a rigid temporal order of events, nor it is meant to be comprehensive. It includes solved examples for a solid understanding. The division into chapters under the names of key players in the development of the field is not intended to separate these individual contributions entirely, but to highlight their different approaches to entropy. This structure helps to provide a different view-point from other text-books on entropy.
Download or read book Entropy and Diversity written by Tom Leinster and published by Cambridge University Press. This book was released on 2021-04-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.
Download or read book Entropy written by Andreas Greven and published by Princeton University Press. This book was released on 2014-09-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book New Foundations for Information Theory written by David Ellerman and published by Springer Nature. This book was released on 2021-10-30 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.
Download or read book The Maximum Entropy Method written by Nailong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forty years ago, in 1957, the Principle of Maximum Entropy was first intro duced by Jaynes into the field of statistical mechanics. Since that seminal publication, this principle has been adopted in many areas of science and technology beyond its initial application. It is now found in spectral analysis, image restoration and a number of branches ofmathematics and physics, and has become better known as the Maximum Entropy Method (MEM). Today MEM is a powerful means to deal with ill-posed problems, and much research work is devoted to it. My own research in the area ofMEM started in 1980, when I was a grad uate student in the Department of Electrical Engineering at the University of Sydney, Australia. This research work was the basis of my Ph.D. the sis, The Maximum Entropy Method and Its Application in Radio Astronomy, completed in 1985. As well as continuing my research in MEM after graduation, I taught a course of the same name at the Graduate School, Chinese Academy of Sciences, Beijingfrom 1987to 1990. Delivering the course was theimpetus for developing a structured approach to the understanding of MEM and writing hundreds of pages of lecture notes.
Download or read book Social Entropy Theory written by Kenneth D. Bailey and published by SUNY Press. This book was released on 1990-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Social Entropy Theory illuminates the fundamental problems of societal analysis with a nonequilibrium approach, a new frame of reference built upon contemporary macrological principles, including general systems theory and information theory. Social entropy theory, using Shannon's H and the entropy concept, avoids the common (and often artificial) separation of theory and method in sociology. The hallmark of the volume is integration, as seen in the author's interdisciplinary discussions of equilibrium, entropy, and homeostasis. Unique features of the book are the introduction of the three-level model of social measurement, the theory of allocation, the concepts of global-mutable-immutable, discussion of order and power, and a large set of testable hypotheses.
Download or read book The Method Of Maximum Entropy written by Henryk Gzyl and published by World Scientific. This book was released on 1995-03-16 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an outgrowth of a set of lecture notes on the maximum entropy method delivered at the 1st Venezuelan School of Mathematics. This yearly event aims at acquainting graduate students and university teachers with the trends, techniques and open problems of current interest. In this book the author reviews several versions of the maximum entropy method and makes its underlying philosophy clear.
Download or read book Approaches to Entropy written by Jeremy R. H. Tame and published by . This book was released on 2019 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about thermodynamics, not history, but it adopts a semi-historical approach in order to highlight different approaches to entropy. The book does not follow a rigid temporal order of events, nor it is meant to be comprehensive. It includes solved examples for a solid understanding. The division into chapters under the names of key players in the development of the field is not intended to separate these individual contributions entirely, but to highlight their different approaches to entropy. This structure helps to provide a different view-point from other text-books on entropy.
Download or read book Maximum Entropy and Ecology written by John Harte and published by OUP Oxford. This book was released on 2011-06-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering graduate textbook provides readers with the concepts and practical tools required to understand the maximum entropy principle, and apply it to an understanding of ecological patterns. Rather than building and combining mechanistic models of ecosystems, the approach is grounded in information theory and the logic of inference. Paralleling the derivation of thermodynamics from the maximum entropy principle, the state variable theory of ecology developed in this book predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species over multiple spatial scales, a wide range of habitats, and diverse taxonomic groups. The first part of the book is foundational, discussing the nature of theory, the relationship of ecology to other sciences, and the concept of the logic of inference. Subsequent sections present the fundamentals of macroecology and of maximum information entropy, starting from first principles. The core of the book integrates these fundamental principles, leading to the derivation and testing of the predictions of the maximum entropy theory of ecology (METE). A final section broadens the book's perspective by showing how METE can help clarify several major issues in conservation biology, placing it in context with other theories and highlighting avenues for future research.
Download or read book Entropy Theory in Hydraulic Engineering written by Vijay P. Singh and published by . This book was released on 2014 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vijay Singh explains the basic concepts of entropy theory from a hydraulic perspective and demonstrates the theory's application in solving practical engineering problems.
Download or read book Statistical Data Analysis and Entropy written by Nobuoki Eshima and published by Springer Nature. This book was released on 2020-01-21 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reconsiders statistical methods from the point of view of entropy, and introduces entropy-based approaches for data analysis. Further, it interprets basic statistical methods, such as the chi-square statistic, t-statistic, F-statistic and the maximum likelihood estimation in the context of entropy. In terms of categorical data analysis, the book discusses the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) for measuring association and/or predictive powers in association models, and generalized linear models (GLMs). Through association and GLM frameworks, it also describes ECC and ECD in correlation and regression analyses for continuous random variables. In multivariate statistical analysis, canonical correlation analysis, T2-statistic, and discriminant analysis are discussed in terms of entropy. Moreover, the book explores the efficiency of test procedures in statistical tests of hypotheses using entropy. Lastly, it presents an entropy-based path analysis for structural GLMs, which is applied in factor analysis and latent structure models. Entropy is an important concept for dealing with the uncertainty of systems of random variables and can be applied in statistical methodologies. This book motivates readers, especially young researchers, to address the challenge of new approaches to statistical data analysis and behavior-metric studies.
Download or read book An Introduction to Transfer Entropy written by Terry Bossomaier and published by Springer. This book was released on 2016-11-15 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance. The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.
Download or read book The Entropy of Capitalism written by Robert Biel and published by BRILL. This book was released on 2011-10-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the context of the ecological crisis of the twenty-first century, the book integrates Marxism and systems theory to reveal finance capital and the ‘war on terror’ as complementary responses of a capitalism reduced to parasitising upon symptoms of chaos.
Download or read book Maximum Entropy and Bayesian Methods written by John Skilling and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge, England, 1988
Download or read book Discover Entropy and the Second Law of Thermodynamics written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Evolution As Entropy written by Daniel R. Brooks and published by University of Chicago Press. This book was released on 1988-10-15 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition in just two years offers a considerably revised second chapter, in which information behavior replaces analogies to purely physical systems, as well as practical applications of the authors' theory. Attention is also given to a hierarchical theory of ecosystem behavior, taking note of constraints on local ecosystem members resul.
Download or read book The Cross Entropy Method written by Reuven Y. Rubinstein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rubinstein is the pioneer of the well-known score function and cross-entropy methods. Accessible to a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist and practitioner, who is interested in smart simulation, fast optimization, learning algorithms, and image processing.
