The Statistical Foundations Of Entropy

Author : John D Ramshaw
Publisher : World Scientific
Page : 216 pages
File Size : 45,5 Mb
Release : 2017-11-24
Category : Science
ISBN : 9789813234147

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The Statistical Foundations Of Entropy by John D Ramshaw Pdf

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.

Author : O. Penrose
Publisher : Elsevier
Page : 270 pages
File Size : 47,7 Mb
Release : 2016-09-21
Category : Science
ISBN : 9781483156484

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Foundations of Statistical Mechanics by O. Penrose Pdf

International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems of statistical mechanics. This book examines the theory that provides explicit recognition to the limitations on one's powers of observation. Organized into six chapters, this volume begins with an overview of the main physical assumptions and their idealization in the form of postulates. This text then examines the consequences of these postulates that culminate in a derivation of the fundamental formula for calculating probabilities in terms of dynamic quantities. Other chapters provide a careful analysis of the significant notion of entropy, which shows the links between thermodynamics and statistical mechanics and also between communication theory and statistical mechanics. The final chapter deals with the thermodynamic concept of entropy. This book is intended to be suitable for students of theoretical physics. Probability theorists, statisticians, and philosophers will also find this book useful.

Author : Petr Jizba,Jan Korbel
Publisher : Unknown
Page : 0 pages
File Size : 44,6 Mb
Release : 2022
Category : Electronic
ISBN : 3036535586

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The Statistical Foundations of Entropy by Petr Jizba,Jan Korbel Pdf

In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann-Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann-Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems.

Author : Roberto Luzzi,Aurea R. Vasconcellos,J. Galvao Ramos
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 45,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783322800190

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Statistical Foundations of Irreversible Thermodynamics by Roberto Luzzi,Aurea R. Vasconcellos,J. Galvao Ramos Pdf

Some aspects of the physics of many-body systems arbitrarily away from equilibrium, mainly the characterization and irreversible evolution of their macroscopic state, are considered. The present status of phenomenological irreversible thermodynamics is described. An approach for building a statistical thermodynamics - dubbed Informational-Statistical-Thermodynamics - based on a non-equilibrium statistical ensemble formalism is presented. The formalism can be considered as encompassed within the scope of the so-called Predictive Statistical Mechanics, in which the predictability of future states in terms of the knowledge of present and past states, and the question of historicity in the case of systems with complex behaviour, is its main characteristic. The book is recommended for researchers in the area of non-equilibrium statistical mechanics and thermodynamics, as well as a textbook for advanced courses for graduate students in the area of condensed matter physics.

Author : Phil Attard
Publisher : Elsevier
Page : 450 pages
File Size : 43,8 Mb
Release : 2002-07-08
Category : Science
ISBN : 9780080519180

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Thermodynamics and Statistical Mechanics by Phil Attard Pdf

The account of thermodynamics and statistical mechanics in Thermodynamics and Statistical Mechanics is based on entropy and its maximization. Building from first principles, it gives a transparent explanation of the physical behaviour of equilibrium thermodynamic systems, and it presents a comprehensive, self-contained account of the modern mathematical and computational techniques of statistical mechanics. This field of study is of vital importance to researchers, lecturers and students alike. Dr Attard is a well-known researcher in statistical mechanics who has made significant contributions to this field. His book offers a fresh perspective on the foundations of statistical thermodynamics. It includes a number of new results and novel derivations, and provides an intriguing alternative to existing monographs. Especially of note are the simple graphs and figures that illustrate the text throughout and the logical organization of the material. Thermodynamics and Statistical Mechanics will be an invaluable and comprehensive reference manual for research scientists. This text can be used as a complement to existing texts and for supplementary reading. Offers a fresh perspective on the foundations of statistical thermodynamics Includes a number of new results and novel derivations, and provides an intriguing alternative to existing monographs Simple graphs and figures illustrate the text throughout Logical organization of material An invaluable and comprehensive reference manual for research scientists Can be used as a complement to existing texts and for supplementary reading

Author : Josiah Willard Gibbs
Publisher : Cambridge University Press
Page : 234 pages
File Size : 50,8 Mb
Release : 1960
Category : History
ISBN : 9781108017022

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Elementary Principles in Statistical Mechanics by Josiah Willard Gibbs Pdf

This 1902 book by the great American mathematician gives his mature vision of thermodynamics and statistical physics.

Author : Ian Ford
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 54,6 Mb
Release : 2013-03-27
Category : Science
ISBN : 9781118597491

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Statistical Physics by Ian Ford Pdf

This undergraduate textbook provides a statistical mechanical foundation to the classical laws of thermodynamics via a comprehensive treatment of the basics of classical thermodynamics, equilibrium statistical mechanics, irreversible thermodynamics, and the statistical mechanics of non-equilibrium phenomena. This timely book has a unique focus on the concept of entropy, which is studied starting from the well-known ideal gas law, employing various thermodynamic processes, example systems and interpretations to expose its role in the second law of thermodynamics. This modern treatment of statistical physics includes studies of neutron stars, superconductivity and the recently developed fluctuation theorems. It also presents figures and problems in a clear and concise way, aiding the student’s understanding.

Author : Hans J. Kreuzer
Publisher : Oxford University Press, USA
Page : 458 pages
File Size : 52,7 Mb
Release : 1981
Category : Language Arts & Disciplines
ISBN : MINN:31951000534030V

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Nonequilibrium Thermodynamics and Its Statistical Foundations by Hans J. Kreuzer Pdf

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 210 pages
File Size : 54,6 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 9780486601472

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Mathematical Foundations of Statistical Mechanics by Aleksandr I?Akovlevich Khinchin Pdf

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.

Author : Arieh Ben-Naim
Publisher : World Scientific
Page : 411 pages
File Size : 43,8 Mb
Release : 2008
Category : Science
ISBN : 9789812707062

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A Farewell to Entropy by Arieh Ben-Naim Pdf

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.

Author : W.T. Grandy Jr.
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400938670

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Foundations of Statistical Mechanics by W.T. Grandy Jr. Pdf

In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].

Author : R. Jancel
Publisher : Elsevier
Page : 440 pages
File Size : 46,8 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483186269

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Foundations of Classical and Quantum Statistical Mechanics by R. Jancel Pdf

Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.

Author : Bernard H. Lavenda
Publisher : Courier Dover Publications
Page : 225 pages
File Size : 46,8 Mb
Release : 2019-04-17
Category : Science
ISBN : 9780486833125

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Nonequilibrium Statistical Thermodynamics by Bernard H. Lavenda Pdf

This book develops in detail the statistical foundations of nonequilibrium thermodynamics, based on the mathematical theory of Brownian motion. Author Bernard H. Lavenda demonstrates that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. His treatment assumes the theory of Brownian motion to be a general and practical model of irreversible processes that are inevitably influenced by random thermal fluctuations. This unifying approach permits the extraction of widely applicable principles from the analysis of specific models. Arranged by argument rather than theory, the text is based on the premises that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes and that they can be viewed as a dynamic superposition of many random events. Intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics, this book will also be of interest to chemical physicists, condensed matter physicists, and readers in the area of nonlinear optics.

Author : M.D. Sturge
Publisher : CRC Press
Page : 480 pages
File Size : 46,9 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781439864425

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Statistical and Thermal Physics by M.D. Sturge Pdf

This book is based on many years of teaching statistical and thermal physics. It assumes no previous knowledge of thermodynamics, kinetic theory, or probability---the only prerequisites are an elementary knowledge of classical and modern physics, and of multivariable calculus. The first half of the book introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. The second half of the book applies these concepts to a wide variety of phenomena, including perfect gases, heat engines, and transport processes. Each chapter contains fully worked examples and real-world problems drawn from physics, astronomy, biology, chemistry, electronics, and mechanical engineering.

Author : Paul Ehrenfest,Tatiana Ehrenfest
Publisher : Courier Corporation
Page : 128 pages
File Size : 53,6 Mb
Release : 2014-11-12
Category : Science
ISBN : 9780486163147

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The Conceptual Foundations of the Statistical Approach in Mechanics by Paul Ehrenfest,Tatiana Ehrenfest Pdf

Classic 1912 article reformulated the foundations of the statistical approach in mechanics. Largely still valid, the treatment covers older formulation of statistico-mechanical investigations, modern formulation of kineto-statistics of the gas model, and more. 1959 edition.