Entropy

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Entropy

Author : Andreas Greven
Publisher : Princeton University Press
ISBN 13 : 1400865220
Total Pages : 376 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Entropy by : Andreas Greven

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.

Anxiety and the Equation

Author : Eric Johnson
Publisher : MIT Press
ISBN 13 : 0262546612
Total Pages : 193 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Anxiety and the Equation by : Eric Johnson

Download or read book Anxiety and the Equation written by Eric Johnson and published by MIT Press. This book was released on 2022-11-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A man and his equation: the anxiety-plagued nineteenth-century physicist who contributed significantly to our understanding of the second law of thermodynamics. Ludwig Boltzmann's grave in Vienna's Central Cemetery bears a cryptic epitaph: S = k log W. This equation was Boltzmann's great discovery, and it contributed significantly to our understanding of the second law of thermodynamics. In Anxiety and the Equation, Eric Johnson tells the story of a man and his equation: the anxiety-plagued nineteenth-century physicist who did his most important work as he struggled with mental illness. Johnson explains that “S” in Boltzmann's equation refers to entropy, and that entropy is the central quantity in the second law of thermodynamics. The second law is always on, running in the background of our lives, providing a way to differentiate between past and future. We know that the future will be a state of higher entropy than the past, and we have Boltzmann to thank for discovering the equation that underlies that fundamental trend. Johnson, accessibly and engagingly, reassembles Boltzmann's equation from its various components and presents episodes from Boltzmann's life—beginning at the end, with “Boltzmann Kills Himself” and “Boltzmann Is Buried (Not Once, But Twice).” Johnson explains the second law in simple terms, introduces key concepts through thought experiments, and explores Boltzmann's work. He argues that Boltzmann, diagnosed by his contemporaries as neurasthenic, suffered from an anxiety disorder. He was, says Johnson, a man of reason who suffered from irrational concerns about his work, worrying especially about opposition from the scientific establishment of the day. Johnson's clear and concise explanations will acquaint the nonspecialist reader with such seemingly esoteric concepts as microstates, macrostates, fluctuations, the distribution of energy, log functions, and equilibrium. He describes Boltzmann's relationships with other scientists, including Max Planck and Henri Poincaré, and, finally, imagines “an alternative ending,” in which Boltzmann lived on and died of natural causes.

Entropy for Biologists

Author : Harold J. Morowitz
Publisher : Elsevier
ISBN 13 : 1483263169
Total Pages : 212 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Entropy for Biologists by : Harold J. Morowitz

Download or read book Entropy for Biologists written by Harold J. Morowitz and published by Elsevier. This book was released on 2013-09-03 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy for Biologists: An Introduction to Thermodynamics is an introductory book for people in the life sciences who wish to master the concepts of thermal physics without being forced to a degree and rate of symbol manipulation which is foreign to their patterns of thought. The book opens with a chapter on temperature, followed by separate chapters that discuss the concepts of energy, kinetic theory, total energy, the second law of thermodynamics, entropy, and probability and information theory. Subsequent chapters deal with statistical mechanics and its relation to thermodynamics, free-energy functions, applications of the Gibbs free energy and the Gibbs chemical potential, and measurement in thermal physics. The book is primarily directed at those graduate and advanced undergraduate students of biology and biochemistry who wish to develop a sense of confidence about their understanding of the thermal physics which will be useful in pursuing their work. It may also prove useful to professionals who wish to bolster their knowledge in this area.

Entropy and Diversity

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1108832709
Total Pages : 457 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Entropy and Diversity by : Tom Leinster

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.

Entropy

Author : Jeremy Rifkin
Publisher : Bantam Books
ISBN 13 : 9780553262995
Total Pages : pages
Book Rating : 4.2/5 (629 download)

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Book Synopsis Entropy by : Jeremy Rifkin

Download or read book Entropy written by Jeremy Rifkin and published by Bantam Books. This book was released on 1981-09-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a hard-hitting analysis of world turmoil and its ceaseless predicaments, according to the thermodynamic law of entropy--all energy flows from order to disorder, from the usable to the unusable

The Biggest Ideas in the Universe

Author : Sean Carroll
Publisher : Penguin
ISBN 13 : 0593186591
Total Pages : 305 pages
Book Rating : 4.5/5 (931 download)

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Book Synopsis The Biggest Ideas in the Universe by : Sean Carroll

Download or read book The Biggest Ideas in the Universe written by Sean Carroll and published by Penguin. This book was released on 2022-09-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: INSTANT NEW YORK TIMES BESTSELLER “Most appealing... technical accuracy and lightness of tone... Impeccable.”—Wall Street Journal “A porthole into another world.”—Scientific American “Brings science dissemination to a new level.”—Science The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers toward grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.

Evolution As Entropy

Author : Daniel R. Brooks
Publisher : University of Chicago Press
ISBN 13 : 9780226075747
Total Pages : 438 pages
Book Rating : 4.0/5 (757 download)

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Book Synopsis Evolution As Entropy by : Daniel R. Brooks

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.

Entropy, Information, and Evolution

Author : Bruce H. Weber
Publisher : MIT Press (MA)
ISBN 13 : 9780262731683
Total Pages : 376 pages
Book Rating : 4.7/5 (316 download)

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Book Synopsis Entropy, Information, and Evolution by : Bruce H. Weber

Download or read book Entropy, Information, and Evolution written by Bruce H. Weber and published by MIT Press (MA). This book was released on 1987-12-01 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting and controversial areas of scientific research in recent years has been the application of the principles of nonequilibrium thermodynamics to the problems of the physical evolution of the universe, the origins of life, the structure and succession of ecological systems, and biological evolution.

Energy and Entropy

Author : Harvey S. Leff
Publisher : CRC Press
ISBN 13 : 1000170365
Total Pages : 303 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Energy and Entropy by : Harvey S. Leff

Download or read book Energy and Entropy written by Harvey S. Leff and published by CRC Press. This book was released on 2020-08-26 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Holographic Entanglement Entropy

Author : Mukund Rangamani
Publisher : Springer
ISBN 13 : 3319525735
Total Pages : 246 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Holographic Entanglement Entropy by : Mukund Rangamani

Download or read book Holographic Entanglement Entropy written by Mukund Rangamani and published by Springer. This book was released on 2017-05-08 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Entropy and Information Theory

Author : Robert M. Gray
Publisher : Springer Science & Business Media
ISBN 13 : 1475739826
Total Pages : 346 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Entropy and Information Theory by : Robert M. Gray

Download or read book Entropy and Information Theory written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Entropy and Its Use

Author : M. Ohya
Publisher : Springer Science & Business Media
ISBN 13 : 9783540208068
Total Pages : 368 pages
Book Rating : 4.2/5 (8 download)

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Book Synopsis Quantum Entropy and Its Use by : M. Ohya

Download or read book Quantum Entropy and Its Use written by M. Ohya and published by Springer Science & Business Media. This book was released on 2004-03-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

Entropy and Negentropy

Author : Edited by: Kisak
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781519182494
Total Pages : 254 pages
Book Rating : 4.1/5 (824 download)

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Book Synopsis Entropy and Negentropy by : Edited by: Kisak

Download or read book Entropy and Negentropy written by Edited by: Kisak and published by Createspace Independent Publishing Platform. This book was released on 2015-11-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder. According to the second law of thermodynamics the entropy of an isolated system never decreases; such a system will spontaneously proceed towards thermodynamic equilibrium, the configuration with maximum entropy. Systems that are not isolated may decrease in entropy, provided they increase the entropy of their environment by at least that same amount. Since entropy is a state function, the change in the entropy of a system is the same for any process that goes from a given initial state to a given final state, whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment.The negentropy, also negative entropy, syntropy, extropy, ectropy or entaxy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life. The concept and phrase "negative entropy" was introduced by Erwin Schr�dinger in his 1944 popular-science book What is Life? Later, L�on Brillouin shortened the phrase to negentropy, to express it in a more "positive" way: a living system imports negentropy and stores it. In 1974, Albert Szent-Gy�rgyi proposed replacing the term negentropy with syntropy.This book discusses the concepts of both entropy and negentropy which can be viewed as the means to an end and a beginning in the world of physics and is designed to be a reference and provide an overview of the topic and give the reader a structured knowledge to familiarize yourself with the topic at the most affordable price possible.The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most current knowledge on the topic, based on the date of publication.

Entropy and Information

Author : Mikhail V. Volkenstein
Publisher : Springer Science & Business Media
ISBN 13 : 303460078X
Total Pages : 210 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Entropy and Information by : Mikhail V. Volkenstein

Download or read book Entropy and Information written by Mikhail V. Volkenstein and published by Springer Science & Business Media. This book was released on 2009-10-27 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Student's Guide to Entropy

Author : Don S. Lemons
Publisher : Cambridge University Press
ISBN 13 : 1107470048
Total Pages : 195 pages
Book Rating : 4.1/5 (74 download)

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Book Synopsis A Student's Guide to Entropy by : Don S. Lemons

Download or read book A Student's Guide to Entropy written by Don S. Lemons and published by Cambridge University Press. This book was released on 2013-08-29 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Around 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

An Introduction to Transfer Entropy

Author : Terry Bossomaier
Publisher : Springer
ISBN 13 : 3319432222
Total Pages : 190 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis An Introduction to Transfer Entropy by : Terry Bossomaier

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.

Simulation with Entropy in Engineering Thermodynamics

Author : Jean Thoma
Publisher : Springer Science & Business Media
ISBN 13 : 3540328513
Total Pages : 141 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Simulation with Entropy in Engineering Thermodynamics by : Jean Thoma

Download or read book Simulation with Entropy in Engineering Thermodynamics written by Jean Thoma and published by Springer Science & Business Media. This book was released on 2007-04-27 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students, academics and researchers will find this book an invaluable contribution to the understanding of thermodynamics. In this new treatment of the subject, the authors focus on the principles of thermodynamic variables and the practical simulation of thermodynamic systems, and endeavor to show how simple thermodynamics really is. It offers a unique view of modern complex systems engineering and its ramifications.