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The Statistical Foundations Of Entropy

The Statistical Foundations Of Entropy
Author: John D Ramshaw
Publisher: World Scientific
Total Pages: 217
Release: 2017-11-24
Genre: Science
ISBN: 9813234148

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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.


The Statistical Foundations of Entropy

The Statistical Foundations of Entropy
Author: Petr Jizba
Publisher: Mdpi AG
Total Pages: 182
Release: 2022-04-06
Genre:
ISBN: 9783036535579

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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.


Foundations of Statistical Mechanics

Foundations of Statistical Mechanics
Author: O. Penrose
Publisher: Elsevier
Total Pages: 272
Release: 2016-09-21
Genre: Science
ISBN: 1483156486

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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.


Foundations of Statistical Mechanics

Foundations of Statistical Mechanics
Author: W.T. Grandy Jr.
Publisher: Springer Science & Business Media
Total Pages: 391
Release: 2012-12-06
Genre: Science
ISBN: 9400938675

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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].


Farewell To Entropy, A: Statistical Thermodynamics Based On Information

Farewell To Entropy, A: Statistical Thermodynamics Based On Information
Author: Arieh Ben-naim
Publisher: World Scientific
Total Pages: 411
Release: 2008-01-18
Genre: Science
ISBN: 9814338281

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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.


Statistical Foundations of Irreversible Thermodynamics

Statistical Foundations of Irreversible Thermodynamics
Author: Roberto Luzzi
Publisher: Springer Science & Business Media
Total Pages: 180
Release: 2013-04-17
Genre: Science
ISBN: 3322800199

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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.


Thermodynamics and Statistical Mechanics

Thermodynamics and Statistical Mechanics
Author: Phil Attard
Publisher: Academic Press
Total Pages: 444
Release: 2002-07-24
Genre: Science
ISBN: 9780120663217

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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.


Statistical Physics

Statistical Physics
Author: Ian Ford
Publisher: John Wiley & Sons
Total Pages: 290
Release: 2013-03-27
Genre: Science
ISBN: 1118597494

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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.


Statistical Mechanics And Scientific Explanation: Determinism, Indeterminism And Laws Of Nature

Statistical Mechanics And Scientific Explanation: Determinism, Indeterminism And Laws Of Nature
Author: Valia Allori
Publisher: World Scientific
Total Pages: 698
Release: 2020-04-22
Genre: Science
ISBN: 9811211736

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The book explores several open questions in the philosophy and the foundations of statistical mechanics. Each chapter is written by a leading expert in philosophy of physics and/or mathematical physics. Here is a list of questions that are addressed in the book:


Statistical Mechanics

Statistical Mechanics
Author: James Sethna
Publisher: OUP Oxford
Total Pages: 374
Release: 2006-04-07
Genre: Science
ISBN: 0191566217

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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.