Entropy And The Time Evolution Of Macroscopic Systems

Author : Walter T. Grandy Jr.
Publisher : OUP Oxford
Page : 225 pages
File Size : 49,8 Mb
Release : 2008-06-26
Category : Science
ISBN : 9780191562952

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Entropy and the Time Evolution of Macroscopic Systems by Walter T. Grandy Jr. Pdf

This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.

Author : Andreas Greven,Gerhard Keller,Gerald Warnecke
Publisher : Princeton University Press
Page : 376 pages
File Size : 49,6 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865222

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Entropy by Andreas Greven,Gerhard Keller,Gerald Warnecke Pdf

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 : Alexander Leonidovich Kuzemsky
Publisher : World Scientific
Page : 484 pages
File Size : 49,6 Mb
Release : 2022-10-14
Category : Science
ISBN : 9789811267024

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Mystery Of Time, The: Asymmetry Of Time And Irreversibility In The Natural Processes by Alexander Leonidovich Kuzemsky Pdf

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time.The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

Author : Gerhard Ernst,Andreas Hüttemann
Publisher : Cambridge University Press
Page : 219 pages
File Size : 46,6 Mb
Release : 2010-01-21
Category : Science
ISBN : 9781139485432

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Time, Chance, and Reduction by Gerhard Ernst,Andreas Hüttemann Pdf

Statistical mechanics attempts to explain the behaviour of macroscopic physical systems in terms of the mechanical properties of their constituents. Although it is one of the fundamental theories of physics, it has received little attention from philosophers of science. Nevertheless, it raises philosophical questions of fundamental importance on the nature of time, chance and reduction. Most philosophical issues in this domain relate to the question of the reduction of thermodynamics to statistical mechanics. This book addresses issues inherent in this reduction: the time-asymmetry of thermodynamics and its absence in statistical mechanics; the role and essential nature of chance and probability in this reduction when thermodynamics is non-probabilistic; and how, if at all, the reduction is possible. Compiling contributions on current research by experts in the field, this is an invaluable survey of the philosophy of statistical mechanics for academic researchers and graduate students interested in the foundations of physics.

Author : Andreas Greven,Gerald Warnecke,Gerhard Keller
Publisher : Unknown
Page : 128 pages
File Size : 49,7 Mb
Release : 2014-08-21
Category : Electronic books
ISBN : 1322063222

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Entropy by Andreas Greven,Gerald Warnecke,Gerhard Keller Pdf

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 : Valia Allori
Publisher : World Scientific
Page : 698 pages
File Size : 45,7 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811211737

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Statistical Mechanics And Scientific Explanation: Determinism, Indeterminism And Laws Of Nature by Valia Allori Pdf

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:

Author : John D Ramshaw
Publisher : World Scientific
Page : 216 pages
File Size : 42,6 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 : Jakob Yngvason
Publisher : European Mathematical Society
Page : 288 pages
File Size : 47,5 Mb
Release : 2008
Category : Biography & Autobiography
ISBN : 3037190574

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Boltzmann's Legacy by Jakob Yngvason Pdf

Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium ``Boltzmann's Legacy'' was held at the Erwin Schrodinger International Institute for Mathematical Physics in June 2006. This text covers a broad spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of today's leading scholars in the field. The book addresses students and researchers in mathematics, physics, and the history of science.

Author : Michael C. Mackey
Publisher : Courier Corporation
Page : 212 pages
File Size : 41,7 Mb
Release : 2003-01-01
Category : Science
ISBN : 0486432432

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Time's Arrow by Michael C. Mackey Pdf

Exploration of Second Law of Thermodynamics details fundamental dynamic properties behind construction of statistical mechanics. Topics include maximal entropy principles; invertible and noninvertible systems; ergodicity and unique equilibria; and asymptotic periodicity and entropy evolution. Geared toward physicists and applied mathematicians; suitable for advanced undergraduate and graduate courses. 1992 edition.

Author : Jochen Rau
Publisher : Oxford University Press
Page : 208 pages
File Size : 45,6 Mb
Release : 2017-09-22
Category : Science
ISBN : 9780192529503

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Statistical Physics and Thermodynamics by Jochen Rau Pdf

Statistical physics and thermodynamics describe the behaviour of systems on the macroscopic scale. Their methods are applicable to a wide range of phenomena: from refrigerators to the interior of stars, from chemical reactions to magnetism. Indeed, of all physical laws, the laws of thermodynamics are perhaps the most universal. This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework. While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises, covering all major topics of a standard course on statistical physics and thermodynamics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814338288

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A Farewell to Entropy by Anonim Pdf

Author : Paul Bracken
Publisher : BoD – Books on Demand
Page : 276 pages
File Size : 41,5 Mb
Release : 2020-10-14
Category : Science
ISBN : 9781839680441

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Quantum Mechanics by Paul Bracken Pdf

Quantum mechanics touches all areas of physics, chemistry, life sciences, and engineering. It has emerged as a tool for researching and developing new technology that has had a deep impact on modern life. An essential ingredient of quantum mechanics is the role of the observer and the duality between particle and wave properties of matter at very small scales. This book covers such topics as complex space forms of quantum mechanics, entropy in quantum mechanics, and equations of relativistic quantum mechanics as well as applications of quantum mechanics to more complicated situations. Written by international experts, the book illustrates the wide scope, influence, and applicability of quantum mechanics.

Author : Michal Pavelka,Václav Klika,Miroslav Grmela
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 48,9 Mb
Release : 2018-08-06
Category : Science
ISBN : 9783110350951

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Multiscale Thermo-Dynamics by Michal Pavelka,Václav Klika,Miroslav Grmela Pdf

One common feature of new emerging technologies is the fusion of the very small (nano) scale and the large scale engineering. The classical environment provided by single scale theories, as for instance by the classical hydrodynamics, is not anymore satisfactory. The main challenge is to keep the important details while still be able to keep the overall picture and simplicity. It is the thermodynamics that addresses this challenge. Our main reason for writing this book is to explain such general viewpoint of thermodynamics and to illustrate it on a very wide range of examples. Contents Levels of description Hamiltonian mechanics Irreversible evolution Reversible and irreversible evolution Multicomponent systems Contact geometry Appendix: Mathematical aspects

Author : Tatiana Aleksandrovna Khantuleva
Publisher : Springer Nature
Page : 347 pages
File Size : 43,6 Mb
Release : 2022-07-18
Category : Science
ISBN : 9789811924040

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Mathematical Modeling of Shock-Wave Processes in Condensed Matter by Tatiana Aleksandrovna Khantuleva Pdf

This book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress–strain relationships derived with relaxation and inertia effect in elastic–plastic transition determines material properties in transient regimes.

Author : C. Lindblad
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 51,8 Mb
Release : 2001-11-30
Category : Science
ISBN : 140200320X

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Non-Equilibrium Entropy and Irreversibility by C. Lindblad Pdf

The problem of deriving irreversible thermodynamics from the re versible microscopic dynamics has been on the agenda of theoreti cal physics for a century and has produced more papers than can be digested by any single scientist. Why add to this too long list with yet another work? The goal is definitely not to give a gen eral review of previous work in this field. My ambition is rather to present an approach differing in some key aspects from the stan dard treatments, and to develop it as far as possible using rather simple mathematical tools (mainly inequalities of various kinds). However, in the course of this work I have used a large number of results and ideas from the existing literature, and the reference list contains contributions from many different lines of research. As a consequence the reader may find the arguments a bit difficult to follow without some previous exposure to this set of problems.