An Introduction to Chaos in Nonequilibrium Statistical Mechanics

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Cambridge University Press, Aug 28, 1999 - Science - 287 pages
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This book is an introduction to the applications in nonequilibrium statistical mechanics of chaotic dynamics, and also to the use of techniques in statistical mechanics important for an understanding of the chaotic behaviour of fluid systems. The fundamental concepts of dynamical systems theory are reviewed and simple examples are given. Advanced topics including SRB and Gibbs measures, unstable periodic orbit expansions, and applications to billiard-ball systems, are then explained. The text emphasises the connections between transport coefficients, needed to describe macroscopic properties of fluid flows, and quantities, such as Lyapunov exponents and Kolmogorov-Sinai entropies, which describe the microscopic, chaotic behaviour of the fluid. Later chapters consider the roles of the expanding and contracting manifolds of hyperbolic dynamical systems and the large number of particles in macroscopic systems. Exercises, detailed references and suggestions for further reading are included.
 

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Contents

1 Nonequilibrium statistical mechanics
1
2 The Boltzmann equation
21
3 Liouvilles equation
49
4 Boltzmanns ergodic hypothesis
58
mixing systems
67
6 The GreenKubo formulae
75
7 The bakers transformation
89
8 Lyapunov exponents bakers map and toral automorphisms
100
12 Transport coefficients and chaos
152
13 SinaiRuelleBowen SRB and Gibbs measures
163
14 Fractal forms in GreenKubo relations
195
15 Unstable periodic orbits
203
16 Lorentz lattice gases
217
17 Dynamical foundations of the Boltzmann equation
227
18 The Boltzmann equation returns
240
19 Whats next ?
257

9 KolmogorovSinai entropy
118
10 The ProbeniusPerron equation
129
11 Open systems and escape rates
136
Bibliography
267
Index
283
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