Preface | p. xi |
List of Contributors | p. xiii |
Introduction | p. 1 |
Outline of the Book | p. 4 |
Notations | p. 14 |
Fundamental Concepts | p. 17 |
Entropy: a Subtle Concept in Thermodynamics | p. 19 |
Origin of Entropy in Thermodynamics | p. 19 |
Mechanical Interpretation of Entropy in the Kinetic Theory of Gases | p. 23 |
Configurational Entropy | p. 25 |
Entropy and Potential Energy of Gravitation | p. 28 |
Planetary Atmospheres | p. 28 |
Pfeffer Tube | p. 29 |
Entropy and Intermolecular Energies | p. 30 |
Entropy and Chemical Energies | p. 32 |
Omissions | p. 34 |
References | p. 35 |
Probabilistic Aspects of Entropy | p. 37 |
Entropy as a Measure of Uncertainty | p. 37 |
Entropy as a Measure of Information | p. 39 |
Relative Entropy as a Measure of Discrimination | p. 40 |
Entropy Maximization under Constraints | p. 43 |
Asymptotics Governed by Entropy | p. 45 |
Entropy Density of Stationary Processes and Fields | p. 48 |
References | p. 52 |
Entropy in Thermodynamics | p. 55 |
Phenomenological Thermodynamics and Entropy Principles | p. 57 |
Introduction | p. 57 |
A Simple Classification of Theories of Continuum Thermodynamics | p. 58 |
Comparison of Two Entropy Principles | p. 63 |
Basic Equations | p. 63 |
Generalized Coleman-Noll Evaluation of the Clausius-Duhem Inequality | p. 66 |
Muller-Liu's Entropy Principle | p. 71 |
Concluding Remarks | p. 74 |
References | p. 75 |
Entropy in Nonequilibrium | p. 79 |
Thermodynamics of Irreversible Processes and Rational Thermodynamics for Viscous, Heat-Conducting Fluids | p. 79 |
Kinetic Theory of Gases, the Motivation for Extended Thermodynamics | p. 82 |
A Remark on Temperature | p. 82 |
Entropy Density and Entropy Flux | p. 83 |
13-Moment Distribution. Maximization of Nonequilibrium Entropy | p. 83 |
Balance Equations for Moments | p. 84 |
Moment Equations for 13 Moments. Stationary Heat Conduction | p. 85 |
Kinetic and Thermodynamic Temperatures | p. 87 |
Moment Equations for 14 Moments. Minimum Entropy Production | p. 89 |
Extended Thermodynamics | p. 93 |
Paradoxes | p. 93 |
Formal Structure | p. 95 |
Pulse Speeds | p. 98 |
Light Scattering | p. 101 |
A Remark on Alternatives | p. 103 |
References | p. 104 |
Entropy for Hyperbolic Conservation Laws | p. 107 |
Introduction | p. 107 |
Isothermal Thermoelasticity | p. 108 |
Hyperbolic Systems of Conservation Laws | p. 110 |
Entropy | p. 113 |
Quenching of Oscillations | p. 117 |
References | p. 119 |
Irreversibility and the Second Law of Thermodynamics | p. 121 |
Three Concepts of (Ir)reversibility | p. 121 |
Early Formulations of the Second Law | p. 124 |
Planck | p. 129 |
Gibbs | p. 132 |
Caratheodory | p. 133 |
Lieb and Yngvason | p. 140 |
Discussion | p. 143 |
References | p. 145 |
The Entropy of Classical Thermodynamics | p. 147 |
A Guide to Entropy and the Second Law of Thermodynamics | p. 148 |
Some Speculations and Open Problems | p. 190 |
Some Remarks about Statistical Mechanics | p. 192 |
References | p. 193 |
Entropy in Stochastic Processes | p. 197 |
Large Deviations and Entropy | p. 199 |
Where Does Entropy Come From? | p. 199 |
Sanov's Theorem | p. 201 |
What about Markov Chains? | p. 202 |
Gibbs Measures and Large Deviations | p. 203 |
Ventcel-Freidlin Theory | p. 205 |
Entropy and Large Deviations | p. 206 |
Entropy and Analysis | p. 209 |
Hydrodynamic Scaling: an Example | p. 211 |
References | p. 214 |
Relative Entropy for Random Motion in a Random Medium | p. 215 |
Introduction | p. 215 |
Motivation | p. 215 |
A Branching Random Walk in a Random Environment | p. 217 |
Particle Densities and Growth Rates | p. 217 |
Interpretation of the Main Theorems | p. 219 |
Solution of the Variational Problem | |
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