Entropy And The Tao Of Counting
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Entropy And The Tao Of Counting
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Author : Kim Sharp
language : en
Publisher: Springer Nature
Release Date : 2019-12-13
Entropy And The Tao Of Counting written by Kim Sharp and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-13 with Science categories.
This book provides a complete and accurate atomic level statistical mechanical explanation of entropy and the second law of thermodynamics. It assumes only a basic knowledge of mechanics and requires no knowledge of calculus. The treatment uses primarily geometric arguments and college level algebra. Quantitative examples are given at each stage to buttress physical understanding. This text is of benefit to undergraduate and graduate students, as well as educators and researchers in the physical sciences (whether or not they have taken a thermodynamics course) who want to understand or teach the atomic/molecular origins of entropy and the second law. It is particularly aimed at those who, due to insufficient mathematical background or because of their area of study, are not going to take a traditional statistical mechanics course.
Entropy And The Tao Of Counting
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Author : Kim Sharp
language : en
Publisher: Springer
Release Date : 2020-02-05
Entropy And The Tao Of Counting written by Kim Sharp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-05 with Science categories.
This book provides a complete and accurate atomic level statistical mechanical explanation of entropy and the second law of thermodynamics. It assumes only a basic knowledge of mechanics and requires no knowledge of calculus. The treatment uses primarily geometric arguments and college level algebra. Quantitative examples are given at each stage to buttress physical understanding. This text is of benefit to undergraduate and graduate students, as well as educators and researchers in the physical sciences (whether or not they have taken a thermodynamics course) who want to understand or teach the atomic/molecular origins of entropy and the second law. It is particularly aimed at those who, due to insufficient mathematical background or because of their area of study, are not going to take a traditional statistical mechanics course.
The Maximum Entropy Method
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Author : Nailong Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Maximum Entropy Method written by Nailong Wu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Entropy Like State Counting Leads To Human Readable Four Color Map Theorem Proof
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Author : Robert Luckett Shuler Jr.
language : en
Publisher: Infinite Study
Release Date :
Entropy Like State Counting Leads To Human Readable Four Color Map Theorem Proof written by Robert Luckett Shuler Jr. and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper we define coloration entropy or flexibility as a count of the possible distinct colorations of a map (planar graph), and show how a guaranteed minimum coloration flexibility changes based on additions at a boundary of the map. The map is 4-colorable as long as the flexibility is positive, even though the proof method does not construct a coloration.
A Farewell To Entropy
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Author : Arieh Ben-Naim
language : en
Publisher: World Scientific
Release Date : 2008
A Farewell To Entropy written by Arieh Ben-Naim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term ?entropy? with a more familiar, meaningful and appropriate term such as information, missing information or uncertainty. This replacement would facilitate the interpretation of the ?driving force? of many processes in terms of informational changes and dispel the mystery that has always enshrouded entropy.It has been 140 years since Clausius coined the term ?entropy?; almost 50 years since Shannon developed the mathematical theory of ?information? ? subsequently renamed ?entropy.? In this book, the author advocates replacing ?entropy? by ?information,? a term that has become widely used in many branches of science.The author also takes a new and bold approach to thermodynamics and statistical mechanics. Information is used not only as a tool for predicting distributions but as the fundamental cornerstone concept of thermodynamics, held until now by the term ?entropy.? The topics covered include the fundamentals of probability and information theory; the general concept of information as well as the particular concept of information as applied in thermodynamics; the re-derivation of the Sackur?Tetrode equation for the entropy of an ideal gas from purely informational arguments; the fundamental formalism of statistical mechanics; and many examples of simple processes the ?driving force? for which is analyzed in terms of information.
From Randomness And Entropy To The Arrow Of Time
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Author : Lena Zuchowski
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-14
From Randomness And Entropy To The Arrow Of Time written by Lena Zuchowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-14 with Philosophy categories.
The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It demonstrates that it is unlikely that high entropy states will coincide with visible disorder, thus disputing any link between the Arrow of Time and visible disorder.
Maximum Entropy In Action
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Author : Brian Buck
language : en
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press
Release Date : 1991
Maximum Entropy In Action written by Brian Buck and has been published by Oxford : Clarendon Press ; New York : Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.
This book is a collection of introductory, interdisciplinary articles and lectures covering the fundamentals of the maximum entropy approach, a powerful new technique that provides a much needed extension of the established principles of rational inference in the sciences. Maximum entropy allows the interpretation of incomplete and "noisy" data, providing a description of the underlying physical systems. It has found application in both practical and theoretical studies ranging from image enhancement to nuclear physics, and from statistical mechanics to economics. The work explores these applications with specific problems of data analysis taken from the physical sciences. It will interest all physical scientists who deal with data and its interpretation, including statisticians and statistical physicists.
The Statistical Foundations Of Entropy
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Author : John D Ramshaw
language : en
Publisher: World Scientific
Release Date : 2017-11-24
The Statistical Foundations Of Entropy written by John D Ramshaw and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-24 with Science categories.
This book presents an innovative unified approach to the statistical foundations of entropy and the fundamentals of equilibrium statistical mechanics. These intimately related subjects are often developed in a fragmented historical manner which obscures the essential simplicity of their logical structure. In contrast, this book critically reassesses and systematically reorganizes the basic concepts into a simpler sequential framework which reveals more clearly their logical relationships. The inherent indistinguishability of identical particles is emphasized, and the resulting unification of classical and quantum statistics is discussed in detail.The discussion is focused entirely on fundamental concepts, so applications are omitted. The book is written at the advanced undergraduate or beginning graduate level, and will be useful as a concise supplement to conventional books and courses in statistical mechanics, thermal physics, and thermodynamics. It is also suitable for self-study by those seeking a deeper and more detailed analysis of the fundamentals.
Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications
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Author : M Zuhair Nashed
language : en
Publisher: World Scientific
Release Date : 2022-08-30
Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications written by M Zuhair Nashed and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-30 with Science categories.
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.
Discover Entropy And The Second Law Of Thermodynamics
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Author :
language : en
Publisher:
Release Date :
Discover Entropy And The Second Law Of Thermodynamics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.