Thermodynamics of Chaotic Systems
An Introduction

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems.

Christian Beck (Author), Friedrich Schögl (Author)

9780521484510, Cambridge University Press

Paperback, published 5 January 1995

308 pages, 47 b/w illus. 4 tables
22.8 x 15.2 x 1.8 cm, 0.437 kg

"...many important ideas are sketched...this monograph will be welcomed by nonmathematicians: no advanced mathematical knowledge is required, and the authors explain complicated concepts by first working out a simple example. Mathematicians will be grateful for the explanations (difficult to find elsewhere) on the terminology from statistical mechanics..." Viviane Baladi

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterise chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics. Among the subjects treated are: probabilistic aspects of chaotic dynamics; the symbolic dynamics technique; information measures, the maximum entropy principle; general thermodynamic relations; spin systems; fractals and multifractals; expansion rate and information loss; the topological pressure; transfer operator methods; and repellers and escape. The more advanced chapters deal with the thermodynamic formalism for expanding maps, the thermodynamic analysis of chaotic systems with several intensive parameters and phase transitions in nonlinear dynamics.

Introduction
Part I. Essentials of Nonlinear Dynamics: 1. Nonlinear mappings
2. Probability in the theory of chaotic systems
3. Symbolic dynamics
Part II. Essentials of Information Theory and Thermodynamics: 4. The Shannon information
5. Further information measures
6. Generalized canonical distributions
7. The fundamental thermodynamic relations
8. Spin systems
Part III. Thermostatistics of Multifractals: 9. Escort distributions
10. Fractals
11. Multifractals
12. Bit cumulants in multifractal distribution
13. Thermodynamics of a finite volume
Part IV. Dynamical Analysis of Chaotic Systems: 14. Statistics of dynamical symbol sequences
15. Expansion rate and information loss
16. The topological pressure
17. Transfer operator methods
18. Repellers and escape
Part V. Advanced Thermodynamics: 19. Thermodynamics of expanding maps
20. Thermodynamics with several intensive parameters
21. Phase transitions.

Subject Areas: Nonlinear science [PBWR]