Entropy

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Princeton University Press, 2003 - Mathematics - 358 pages
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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.

 

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Contents

Introduction
1
Fundamental Concepts
17
Entropy a Subtle Concept in Thermodynamics
19
Probabilistic Aspects of Entropy
37
Entropy in Thermodynamics
55
Phenomenological Thermodynamics and Entropy Principles
57
Entropy in Nonequilibrium
79
Entropy for Hyperbolic Conservation Laws
107
Large Deviations and Entropy
199
Relative Entropy for Random Motion in a Random Medium
215
Metastability and Entropy
233
Entropy Production in Driven Spatially Extended Systems
251
Entropy a Dialogue
269
Entropy and Information
277
Classical and Quantum Entropies Dynamics and Information
279
Complexity and Information in Data
299

Irreversibility and the Second Law of Thermodynamics
121
The Entropy of Classical Thermodynamics
147
Entropy in Stochastic Processes
197
Entropy in Dynamical Systems
313
Entropy in Ergodic Theory
329
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About the author (2003)

In diesem Buch hat Herr Gerhard Keller die wichtigsten vielschichtigen privaten und dienstlichen Ereignisse, Aktivitaten und Unternehmungen aus seinem bisherigen Leben Revue passieren lassen.

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