Thermodynamics of Chaotic Systems
An Introduction
Published on 1. July 1993
Book
Hardback
306 pages
978-0-521-43367-9 (ISBN)
Description
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.
Reviews / Votes
"...for theoreticians interested in critical phenomena and related subjects, it is well worth reading and rereading...highly recommended for both individuals and libraries." R.J. Becker, Applied Merchanics Review "...well-written and clearly organized. The authors have tried to write a pedagogical introduction, and for the most part have succeeded...accessible to a wide audience....the presentation is concise in a way that brings out the basic structure of the theory. There is a clear place for an introductory book written in this style in a field like the thermodynamics of chaos, where the primary literature is mainly concerned with detail...I enjoyed reading this excellent book. I can easily recommend it to any reader who finds the subject matter of interest. Its pedagogical quality makes it accessible to the interested novice and its clarity of organization will make it useful to experts." Joseph Bryngelson, Journal of Statistical Physics "...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 BaladiMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
4 Tables, unspecified; 47 Line drawings, unspecified
Dimensions
Height: 235 mm
Width: 156 mm
Thickness: 21 mm
Weight
573 gr
ISBN-13
978-0-521-43367-9 (9780521433679)
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Schweitzer Classification
Other editions
New editions
Book
01/1995
Cambridge University Press
€91.80
Shipment within 15-20 days
Additional editions
Book
01/1995
Cambridge University Press
€91.80
Shipment within 15-20 days
Persons
Content
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.