Thermodynamics of Chaotic Systems An Introduction

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.

The book is written for students and scientists working in physics and related fields. It deals with thermodynamic methods used in nonlinear dynamics, a special branch of statistical physics. An easily readable introduction, the book can also be used as a textbook for special courses.