On The Utility Of Entropy Maximization

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Introductory Statistical Thermodynamics

Author : Nils Dalarsson
Publisher : Academic Press
ISBN 13 : 0123849578
Total Pages : 409 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Introductory Statistical Thermodynamics by : Nils Dalarsson

Download or read book Introductory Statistical Thermodynamics written by Nils Dalarsson and published by Academic Press. This book was released on 2011-01-26 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Statistical Thermodynamics is a text for an introductory one-semester course in statistical thermodynamics for upper-level undergraduate and graduate students in physics and engineering. The book offers a high level of detail in derivations of all equations and results. This information is necessary for students to grasp difficult concepts in physics that are needed to move on to higher level courses. The text is elementary, self contained, and mathematically well-founded, containing a number of problems with detailed solutions to help students to grasp the more difficult theoretical concepts. - Beginning chapters place an emphasis on quantum mechanics - Includes problems with detailed solutions and a number of detailed theoretical derivations at the end of each chapter - Provides a high level of detail in derivations of all equations and results

Maximum-Entropy and Bayesian Methods in Science and Engineering

Author : G. Erickson
Publisher : Springer Science & Business Media
ISBN 13 : 9789027727930
Total Pages : 338 pages
Book Rating : 4.7/5 (279 download)

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Book Synopsis Maximum-Entropy and Bayesian Methods in Science and Engineering by : G. Erickson

Download or read book Maximum-Entropy and Bayesian Methods in Science and Engineering written by G. Erickson and published by Springer Science & Business Media. This book was released on 1988-08-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Maximum Entropy and Ecology

Author : John Harte
Publisher : OUP Oxford
ISBN 13 : 0191621161
Total Pages : 282 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Maximum Entropy and Ecology by : John Harte

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 282 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.

Thermodynamics and Statistical Mechanics

Author : Phil Attard
Publisher : Academic Press
ISBN 13 : 9780120663217
Total Pages : 444 pages
Book Rating : 4.6/5 (632 download)

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Book Synopsis Thermodynamics and Statistical Mechanics by : Phil Attard

Download or read book Thermodynamics and Statistical Mechanics written by Phil Attard and published by Academic Press. This book was released on 2002-07-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isolated systems and thermal equilibrium -- Various reservoirs -- Probability and the general formalism -- Classical statistical mechanics -- Ideal systems -- Interacting particles -- Diagrammatic and functional expansions -- Pair functions -- Functional and perturbation theory -- Inhomogeneous systems -- Coulomb systems -- Computer simulations.

Entropy Measures, Maximum Entropy Principle and Emerging Applications

Author : Karmeshu
Publisher : Springer
ISBN 13 : 3540362126
Total Pages : 300 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Entropy Measures, Maximum Entropy Principle and Emerging Applications by : Karmeshu

Download or read book Entropy Measures, Maximum Entropy Principle and Emerging Applications written by Karmeshu and published by Springer. This book was released on 2012-10-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.

Entropy in Urban and Regional Modelling (Routledge Revivals)

Author : Alan Wilson
Publisher : Routledge
ISBN 13 : 1136498524
Total Pages : 175 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Entropy in Urban and Regional Modelling (Routledge Revivals) by : Alan Wilson

Download or read book Entropy in Urban and Regional Modelling (Routledge Revivals) written by Alan Wilson and published by Routledge. This book was released on 2013-01-11 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1970, this groundbreaking investigation into Entropy in Urban and Regional Modelling provides an extensive and detailed insight into the entropy maximising method in the development of a whole class of urban and regional models. The book has its origins in work being carried out by the author in 1966, when he realised that the well-known gravity model could be derived on the basis of an analogy with statistical, rather than Newtonian, mechanics. Subsequent investigation demonstrated that the entropy maximising method stems from an even higher level of generality, and the beginning of the book is devoted to an account of its importance and use as a general modelling tool. This reissue will be welcomed by a range of students and professionals from fields as diverse as urban and regional studies, economics, geography, planning, civil engineering, mathematics and statistics.

Non-Equilibrium Statistical Mechanics

Author : Ilya Prigogine
Publisher : Courier Dover Publications
ISBN 13 : 0486815552
Total Pages : 337 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Non-Equilibrium Statistical Mechanics by : Ilya Prigogine

Download or read book Non-Equilibrium Statistical Mechanics written by Ilya Prigogine and published by Courier Dover Publications. This book was released on 2017-03-17 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groundbreaking monograph by Nobel Prize winner for researchers and graduate students covers Liouville equation, anharmonic solids, Brownian motion, weakly coupled gases, scattering theory and short-range forces, general kinetic equations, more. 1962 edition.

Entropy and Energy Dissipation in Water Resources

Author : V.P. Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9401124302
Total Pages : 583 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Entropy and Energy Dissipation in Water Resources by : V.P. Singh

Download or read book Entropy and Energy Dissipation in Water Resources written by V.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the landmark contributions of C. E. Shannon in 1948, and those of E. T. Jaynes about a decade later, applications of the concept of entropy and the principle of maximum entropy have proliterated in science and engineering. Recent years have witnessed a broad range of new and exciting developments in hydrology and water resources using the entropy concept. These have encompassed innovative methods for hydrologic network design, transfer of information, flow forecasting, reliability assessment for water distribution systems, parameter estimation, derivation of probability distributions, drainage-network analysis, sediment yield modeling and pollutant loading, bridge-scour analysis, construction of velocity profiles, comparative evaluation of hydrologic models, and so on. Some of these methods hold great promise for advancement of engineering practice, permitting rational alternatives to conventional approaches. On the other hand, the concepts of energy and energy dissipation are being increasingly applied to a wide spectrum of problems in environmental and water resources. Both entropy and energy dissipation have their origin in thermodynamics, and are related concepts. Yet, many of the developments using entropy seem to be based entirely on statistical interpretation and have seemingly little physical content. For example, most of the entropy-related developments and applications in water resources have been based on the information-theoretic interpretation of entropy. We believe if the power of the entropy concept is to be fully realized, then its physical basis has to be established.

E.T. Jaynes

Author : Edwin T. Jaynes
Publisher : Springer Science & Business Media
ISBN 13 : 9780792302131
Total Pages : 468 pages
Book Rating : 4.3/5 (21 download)

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Book Synopsis E.T. Jaynes by : Edwin T. Jaynes

Download or read book E.T. Jaynes written by Edwin T. Jaynes and published by Springer Science & Business Media. This book was released on 1989-04-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Maximum Entropy and Bayesian Methods in Applied Statistics

Author : James H. Justice
Publisher : Cambridge University Press
ISBN 13 : 9780521096034
Total Pages : 0 pages
Book Rating : 4.0/5 (96 download)

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Book Synopsis Maximum Entropy and Bayesian Methods in Applied Statistics by : James H. Justice

Download or read book Maximum Entropy and Bayesian Methods in Applied Statistics written by James H. Justice and published by Cambridge University Press. This book was released on 2009-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers by leading researchers in their respective fields contains contributions showing the use of the maximum entropy method in many of the fields in which it finds application. In the physical, mathematical and biological sciences it is often necessary to make inferences based on insufficient data. The problem of choosing one among the many possible conclusions or models which are compatible with the data may be resolved in a variety of ways. A particularly appealing method is to choose the solution which maximizes entropy in the sense that the conclusion or model honours the observed data but implies no further assumptions not warranted by the data. The maximum entropy principle has been growing in importance and acceptance in many fields, perhaps most notably statistical physics, astronomy, geophysics, signal processing, image analysis and physical chemistry. The papers included in this volume touch on most of the current areas of research activity and application, and will be of interest to research workers in all fields in which the maximum entropy method may be applied.

Information Theory and the Central Limit Theorem

Author : Oliver Thomas Johnson
Publisher : World Scientific
ISBN 13 : 1860944736
Total Pages : 224 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Information Theory and the Central Limit Theorem by : Oliver Thomas Johnson

Download or read book Information Theory and the Central Limit Theorem written by Oliver Thomas Johnson and published by World Scientific. This book was released on 2004 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.

Logarithmic Image Processing: Theory and Applications

Author :
Publisher : Academic Press
ISBN 13 : 0128052295
Total Pages : 320 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Logarithmic Image Processing: Theory and Applications by :

Download or read book Logarithmic Image Processing: Theory and Applications written by and published by Academic Press. This book was released on 2016-07-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logarithmic Image Processing: Theory and Applications, the latest volume in the series that merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy and features cutting-edge articles on recent developments in all areas of microscopy, digital image processing, and many related subjects in electron physics. - Merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy into a single volume - Contains the latest information on logarithmic image processing and its theory and applications - Features cutting-edge articles on recent developments in all areas of microscopy, digital image processing, and many related subjects in electron physics

The Method Of Maximum Entropy

Author : Henryk Gzyl
Publisher : World Scientific
ISBN 13 : 9814501921
Total Pages : 161 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The Method Of Maximum Entropy by : Henryk Gzyl

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.

Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Author : Adriano Polpo
Publisher : Springer
ISBN 13 : 9783319911427
Total Pages : 304 pages
Book Rating : 4.9/5 (114 download)

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Book Synopsis Bayesian Inference and Maximum Entropy Methods in Science and Engineering by : Adriano Polpo

Download or read book Bayesian Inference and Maximum Entropy Methods in Science and Engineering written by Adriano Polpo and published by Springer. This book was released on 2018-07-14 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings from the 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2017), held in São Carlos, Brazil, aim to expand the available research on Bayesian methods and promote their application in the scientific community. They gather research from scholars in many different fields who use inductive statistics methods and focus on the foundations of the Bayesian paradigm, their comparison to objectivistic or frequentist statistics counterparts, and their appropriate applications. Interest in the foundations of inductive statistics has been growing with the increasing availability of Bayesian methodological alternatives, and scientists now face much more difficult choices in finding the optimal methods to apply to their problems. By carefully examining and discussing the relevant foundations, the scientific community can avoid applying Bayesian methods on a merely ad hoc basis. For over 35 years, the MaxEnt workshops have explored the use of Bayesian and Maximum Entropy methods in scientific and engineering application contexts. The workshops welcome contributions on all aspects of probabilistic inference, including novel techniques and applications, and work that sheds new light on the foundations of inference. Areas of application in these workshops include astronomy and astrophysics, chemistry, communications theory, cosmology, climate studies, earth science, fluid mechanics, genetics, geophysics, machine learning, materials science, medical imaging, nanoscience, source separation, thermodynamics (equilibrium and non-equilibrium), particle physics, plasma physics, quantum mechanics, robotics, and the social sciences. Bayesian computational techniques such as Markov chain Monte Carlo sampling are also regular topics, as are approximate inferential methods. Foundational issues involving probability theory and information theory, as well as novel applications of inference to illuminate the foundations of physical theories, are also of keen interest.

The Cross-Entropy Method

Author : Reuven Y. Rubinstein
Publisher : Springer Science & Business Media
ISBN 13 : 1475743211
Total Pages : 316 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Cross-Entropy Method by : Reuven Y. Rubinstein

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.

The Mathematical Theory of Communication

Author : Claude E Shannon
Publisher : University of Illinois Press
ISBN 13 : 025209803X
Total Pages : 141 pages
Book Rating : 4.2/5 (52 download)

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Book Synopsis The Mathematical Theory of Communication by : Claude E Shannon

Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Statistical Mechanics

Author : James Sethna
Publisher : OUP Oxford
ISBN 13 : 0191566217
Total Pages : 374 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Statistical Mechanics by : James Sethna

Download or read book Statistical Mechanics written by James Sethna and published by OUP Oxford. This book was released on 2006-04-07 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.