Entropy

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Energy and Entropy

Energy and Entropy Pdf/ePub eBook Author: ,
Editor: CRC Press
ISBN: 1000170349
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Energy and Entropy by , Summary

Energy is typically regarded as understandable, despite its multiple forms of storage and transfer. Entropy, however, is an enigma, in part because of the common view that it represents disorder. That view is flawed and hides entropy’s connection with energy. In fact, macroscopic matter stores internal energy, and that matter’s entropy is determined by how the energy is stored. Energy and entropy are intimately linked. Energy and Entropy: A Dynamic Duo illuminates connections between energy and entropy for students, teachers, and researchers. Conceptual understanding is emphasised where possible through examples, analogies, figures, and key points. Features: Qualitative demonstration that entropy is linked to spatial and temporal energy spreading, with equilibrium corresponding to the most equitable distribution of energy, which corresponds to maximum entropy Analysis of energy and entropy of matter and photons, with examples ranging from rubber bands, cryogenic cooling, and incandescent lamps to Hawking radiation of black holes Unique coverage of numerical entropy, the 3rd law of thermodynamics, entropic force, dimensionless entropy, free energy, and fluctuations, from Maxwell's demon to Brownian ratchets, plus attempts to violate the second law of thermodynamics

Entropy and Information

Entropy and Information Pdf/ePub eBook Author: Mikhail V. Volkenstein
Editor: Springer Science & Business Media
ISBN: 9783034600781
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Entropy and Information by Mikhail V. Volkenstein Summary

This is just...entropy, he said, thinking that this explained everything, and he repeated the strange word a few times. 1 ? Karel Capek , “Krakatit” This “strange word” denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more universal concept, of fundamental signi?cance for chemistry and biology, as well as physics. Although the concept of energy is usually considered more important and easier to grasp, it turns out, as we shall see, that the idea of entropy is just as substantial—and moreover not all that complicated. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. Furthermore, entropy has remarkable properties. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium. Thereis a surprisingconnectionbetween entropyandinformation,thatis,thetotalintelligencecommunicatedbyamessage. All of this is expounded in the present book, thereby conveying informationto the readeranddecreasinghis entropy;butitis uptothe readertodecidehowvaluable this information might be.

Entropy

Entropy Pdf/ePub eBook Author: ,
Editor: Macmillan International Higher Education
ISBN: 134915380X
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Entropy and Information Theory

Entropy and Information Theory Pdf/ePub eBook Author: Robert M. Gray
Editor: Springer Science & Business Media
ISBN: 1475739826
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Entropy and Information Theory by Robert M. Gray Summary

This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.

Entropy and the Time Evolution of Macroscopic Systems

Entropy and the Time Evolution of Macroscopic Systems Pdf/ePub eBook Author: Grandy Jr.
Editor: OUP Oxford
ISBN: 0191562955
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Entropy and the Time Evolution of Macroscopic Systems by Grandy Jr. Summary

This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.

Entropy, Large Deviations, and Statistical Mechanics

Entropy, Large Deviations, and Statistical Mechanics Pdf/ePub eBook Author: Richard.S. Ellis
Editor: Springer Science & Business Media
ISBN: 1461385334
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Entropy, Large Deviations, and Statistical Mechanics by Richard.S. Ellis Summary

This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of indepen dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure conver gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.

Entropy and Energy

Entropy and Energy Pdf/ePub eBook Author: Ingo Müller,Wolf Weiss
Editor: Springer Science & Business Media
ISBN: 3540323805
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Entropy and Energy by Ingo Müller,Wolf Weiss Summary

Introductory textbook introducing the concept of competition of entropy and energy with various examples. Thermodynamics textbook explaining the roles of entropy and energy as prime movers of nature.

Gray Level Image Threshold Using Neutrosophic Shannon Entropy

Gray Level Image Threshold Using Neutrosophic Shannon Entropy Pdf/ePub eBook Author: Vasile Patrascu
Editor: Infinite Study
ISBN:
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Gray Level Image Threshold Using Neutrosophic Shannon Entropy by Vasile Patrascu Summary

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defi ned taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The effcacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

Entropy Based Design and Analysis of Fluids Engineering Systems

Entropy Based Design and Analysis of Fluids Engineering Systems Pdf/ePub eBook Author: Greg F. Naterer,Jose A. Camberos
Editor: CRC Press
ISBN: 9781420006919
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Entropy Based Design and Analysis of Fluids Engineering Systems by Greg F. Naterer,Jose A. Camberos Summary

From engineering fluid mechanics to power systems, information coding theory and other fields, entropy is key to maximizing performance in engineering systems. It serves a vital role in achieving the upper limits of efficiency of industrial processes and quality of manufactured products. Entropy based design (EBD) can shed new light on various flow processes, ranging from optimized flow configurations in an aircraft engine to highly ordered crystal structures in a turbine blade. Entropy Based Design of Fluid Engineering Systems provides an overview of EBD as an emerging technology with applications to aerospace, microfluidics, heat transfer, and other disciplines. The text extends past analytical methods of Entropy Generation Minimization to numerical simulations involving more complex configurations and experimental measurement techniques. The book begins with an extensive development of basic concepts, including the mathematical properties of entropy and exergy, as well as statistical and numerical formulations of the second law. It then goes on to describe topics related to incompressible flows and the Second Law in microfluidic systems. The authors develop computational and experimental methods for identifying problem regions within a system through the local rates of entropy production. With these techniques, designers can use EBD to focus on particular regions where design modifications can be made to improve system performance. Numerous case studies illustrate the concepts in each chapter, and cover an array of applications including supersonic flows, condensation and turbulence. A one-of-a-kind reference, Entropy Based Design of Fluid Engineering Systems outlines new advances showing how local irreversibilities can be detected in complex configurations so that engineering devices can be re-designed locally to improve overall performance.

The Entropy Principle

The Entropy Principle Pdf/ePub eBook Author: André Thess
Editor: Springer Science & Business Media
ISBN: 9783642133497
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The Entropy Principle by André Thess Summary

Entropy – the key concept of thermodynamics, clearly explained and carefully illustrated. This book presents an accurate definition of entropy in classical thermodynamics which does not “put the cart before the horse” and is suitable for basic and advanced university courses in thermodynamics. Entropy is the most important and at the same time the most difficult term of thermodynamics to understand. Many students are discontent with its classical definition since it is either based on “temperature” and “heat” which both cannot be accurately defined without entropy, or since it includes concepts such as “molecular disorder” which does not fit in a macroscopic theory. The physicists Elliott Lieb and Jakob Yngvason have recently developed a new formulation of thermodynamics which is free of these problems. The Lieb-Yngvason formulation of classical thermodynamics is based on the concept of adiabatic accessibility and culminates in the entropy principle. The entropy principle represents the accurate mathematical formulation of the second law of thermodynamics. Temperature becomes a derived quantity whereas ”heat” is no longer needed. This book makes the Lieb-Yngvason theory accessible to students. The presentation is supplemented by seven illustrative examples which explain the application of entropy and the entropy principle in practical problems in science and engineering.

Entropy, Search, Complexity

Entropy, Search, Complexity Pdf/ePub eBook Author: Imre Csiszár,Gyula O.H. Katona,Gabor Tardos
Editor: Springer Science & Business Media
ISBN: 3540327770
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Entropy, Search, Complexity by Imre Csiszár,Gyula O.H. Katona,Gabor Tardos Summary

This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. The book will be useful to experienced researchers as well as young scientists and students both in mathematics and computer science.

Beyond the Second Law

Beyond the Second Law Pdf/ePub eBook Author: Roderick C. Dewar,Charles H. Lineweaver,Robert K. Niven,Klaus Regenauer-Lieb
Editor: Springer
ISBN: 3642401546
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Beyond the Second Law by Roderick C. Dewar,Charles H. Lineweaver,Robert K. Niven,Klaus Regenauer-Lieb Summary

The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, evolutionary biology and technology, fluid turbulence, microbial biogeochemistry, plasma physics, and radiative transport, using a wide variety of analytical and experimental techniques. Beyond The Second Law will appeal to students and researchers wishing to gain an understanding of entropy production and its central place in the science of non-equilibrium systems – both in detail and in terms of the bigger picture.

The Comedy of Entropy

The Comedy of Entropy Pdf/ePub eBook Author: Patrick O'Neill
Editor: University of Toronto Press
ISBN: 1487586493
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The Comedy of Entropy by Patrick O'Neill Summary

Entropic comedy is the phrase coined by Patrick O'Neill in this study to identify a particular mode of twentieth-century narrative that is not generally recognized. He describes it as the narrative expression of forms of decentred humour, or what might more loosely be called 'black humour.' O'Neill begins his investigation by examining the rise of an essentially new form of humour over the last three hundred years or so in the context of a rapid decay of confidence in traditional authoritative value systems. O'Neill analyses the resulting reorganization of the spectrum of humour, and examines th implications of this for the ways in which we read texts and the world we live in. He then turns from intellectual history to narratology and considers the relationship, in theoretical terms, of homour, play, and narrative as systems of discourse and the role of the reader as a textualizing agent. Finally, he considers some dozen twentieth-century narratives in French, German, and English (with occasional reference to other literatures) in the context of those historical and theoretical concerns. Authors of the texts analysed include Céline, Camus, Satre, and Robbe-Grillet in French; Heller, Beckett, Pynchon, Nabokov, and Joyce in English; Grass, Kafka, and Handke in German. The analyses proceed along lines suggested by structuralist, semiotic, and post-structuraist narrative and literary theory. From his analyses of these works O'Neill concludes they illustrate in narrative terms a mode of modern writing definable as entropic comedy, and he develops a taxonomy of the mode.

The Entropy Crisis

The Entropy Crisis Pdf/ePub eBook Author: ,
Editor:
ISBN: 9814472212
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Entropy, Water and Resources

Entropy, Water and Resources Pdf/ePub eBook Author: Horst Niemes,Mario Schirmer
Editor: Springer Science & Business Media
ISBN: 9783790824162
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Entropy, Water and Resources by Horst Niemes,Mario Schirmer Summary

This book lies at the intersection of natural sciences, economics, and water en- neering and is in line with the long tradition of environmental economics at the University of Heidelberg. In the 1970s, the Neo-Austrian Capital Theory was developed using the fundamental laws of thermodynamics as a common language between the natural and social sciences. Niemes (1981) integrated the dynamic and irreversibility characteristics of the natural environment into the Neo-Austrian c- ital theory. Faber et al. (1983, 1987, 1995) then extended this interdisciplinary approach further to create a comprehensive, dynamic, environmental resource model. Over the last 3 decades, the theoretical foundations of environmental economics have been modi ed and there have been an impressive variety of applications. This book aims to reduce the gaps between economic theory, natural sciences, and engineering practice. One of the reasons these gaps exist is because economic assumptions are used to construct dynamic environmental and resource models, which are not consistent with the fundamental laws of the natural sciences. Another reason for the gap might be the distance between academic theory and real world situations. Based on an extended thermodynamic approach, the authors explain which economic assumptions are acceptable for constructing a dynamic model that is consistent with the natural sciences. In particular, the special role of water in the production and reproduction activities will be considered as an integral component.

Entropy Demystified

Entropy Demystified Pdf/ePub eBook Author: ,
Editor: World Scientific
ISBN: 9814338397
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Entropy, neutro-entropy and anti-entropy for neutrosophic information

Entropy, neutro-entropy and anti-entropy for neutrosophic information Pdf/ePub eBook Author: Vasile Patrascu
Editor: Infinite Study
ISBN:
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Entropy, neutro-entropy and anti-entropy for neutrosophic information by Vasile Patrascu Summary

This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.

Entropy for Smart Kids and their Curious Parents

Entropy for Smart Kids and their Curious Parents Pdf/ePub eBook Author: Arieh Ben-Naim
Editor: Cambridge Scholars Publishing
ISBN: 1527534693
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Entropy for Smart Kids and their Curious Parents by Arieh Ben-Naim Summary

This book discusses entropy and the Second Law of Thermodynamics in such a way that everyone can understand its subject matter. Entropy is one of the most interesting concepts in physics. Although it is a well-defined concept, it is still perceived by even well-known scientists as a concept cloaked in mystery. It is also the most misused, and often abused, concept in physics. In order to understand entropy, one needs to understand the Shannon measure of information, and in order to grasp this idea, one must be familiar with some basic concepts of probability. Therefore, this book consists of three chapters: the first discusses probability, the second addresses Information Theory, and the third considers entropy and the Second Law of Thermodynamics. Readers will discover that the Second Law is nothing but a law of probability.

Maximum-Entropy and Bayesian Methods in Science and Engineering

Maximum-Entropy and Bayesian Methods in Science and Engineering Pdf/ePub eBook Author: G. Erickson,C.R. Smith
Editor: Springer Science & Business Media
ISBN: 9400930496
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Maximum-Entropy and Bayesian Methods in Science and Engineering by G. Erickson,C.R. Smith Summary

This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.