Entropy

Author : Andreas Greven
Publisher : Princeton University Press
ISBN 13 : 1400865220
Total Pages : 376 pages
Book Rating : 4.22/5 ( download)

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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.

Author : Eric Johnson
Publisher : MIT Press
ISBN 13 : 0262546612
Total Pages : 193 pages
Book Rating : 4.14/5 ( download)

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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.

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1108832709
Total Pages : 457 pages
Book Rating : 4.00/5 ( download)

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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.

Author : Sean Carroll
Publisher : Penguin
ISBN 13 : 0593186583
Total Pages : 305 pages
Book Rating : 4.89/5 ( download)

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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.

Author : Mikhail V. Volkenstein
Publisher : Springer Science & Business Media
ISBN 13 : 303460078X
Total Pages : 210 pages
Book Rating : 4.81/5 ( download)

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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.

Author : Terry Bossomaier
Publisher : Springer
ISBN 13 : 3319432222
Total Pages : 190 pages
Book Rating : 4.29/5 ( download)

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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.

Author : Jeremy Rifkin
Publisher : Bantam Books
ISBN 13 : 9780553262995
Total Pages : pages
Book Rating : 4.98/5 ( download)

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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

Author : M. Ohya
Publisher : Springer Science & Business Media
ISBN 13 : 9783540208068
Total Pages : 368 pages
Book Rating : 4.62/5 ( download)

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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.

Author : Robert M. Gray
Publisher : Springer Science & Business Media
ISBN 13 : 1475739826
Total Pages : 346 pages
Book Rating : 4.24/5 ( download)

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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.

Author : André Thess
Publisher : Springer Science & Business Media
ISBN 13 : 3642133495
Total Pages : 186 pages
Book Rating : 4.97/5 ( download)

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Download or read book The Entropy Principle written by André Thess and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.