An introduction to chaos in nonequilibrium statistical mechanics:
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
1999
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| Schriftenreihe: | Cambridge lecture notes in physics
14 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 287 pages) |
| ISBN: | 9780511628870 |
| DOI: | 10.1017/CBO9780511628870 |
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| 100 | 1 | |a Dorfman, J. Robert |d 1937- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to chaos in nonequilibrium statistical mechanics |c J.R. Dorfman |
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| 490 | 0 | |a Cambridge lecture notes in physics |v 14 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |t Nonequilibrium statistical mechanics |t The law of large numbers and the laws of mechanics |t Boltzmann's ergodic hypothesis |t Gibbs' mixing hypothesis |t Irregular dynamical motions |t Modern nonequilibrium statistical mechanics |t Outline of this book |t The Boltzmann equation |t Heuristic derivation |t Boltzmann's H-theorem |t Kac's ring model |t Tagged particle diffusion |t Liouville's equation |t Derivation |t The BBGKY hierarchy equations |t Poincare recurrence theorem |t Boltzmann's ergodic hypothesis |t Equal times in regions of equal measure |t The individual ergodic theorem |t Gibbs' picture: mixing systems |t The definition of a mixing system |t Distribution functions for mixing systems |t Chaos |t The Green--Kubo formulae |t Linear response theory |t van Kampen's objections |t The Green--Kubo formula: diffusion |t The baker's transformation |t The transformation and its properties |t A model Boltzmann equation |t Bernoulli sequences |t Lyapunov exponents, baker's map, and toral automorphisms |t Definition of Lyapunov exponents |t The baker's transformation is ergodic |t The baker's transformation and irreversibility |t The Arnold cat map |t Kolmogorov--Sinai entropy |t Heuristic considerations |t The definition of the KS entropy |t Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem |t The Frobenius--Perron equation |t One-dimensional systems |t The Frobenius--Perron equation in higher dimensions |t Open systems and escape rates |t The escape-rate formalism |t The Smale horseshoe |
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Datensatz im Suchindex
| _version_ | 1804176884343242752 |
|---|---|
| any_adam_object | |
| author | Dorfman, J. Robert 1937- |
| author_facet | Dorfman, J. Robert 1937- |
| author_role | aut |
| author_sort | Dorfman, J. Robert 1937- |
| author_variant | j r d jr jrd |
| building | Verbundindex |
| bvnumber | BV043941990 |
| classification_rvk | UG 2000 UG 3500 UG 3900 |
| collection | ZDB-20-CBO |
| contents | Nonequilibrium statistical mechanics The law of large numbers and the laws of mechanics Boltzmann's ergodic hypothesis Gibbs' mixing hypothesis Irregular dynamical motions Modern nonequilibrium statistical mechanics Outline of this book The Boltzmann equation Heuristic derivation Boltzmann's H-theorem Kac's ring model Tagged particle diffusion Liouville's equation Derivation The BBGKY hierarchy equations Poincare recurrence theorem Equal times in regions of equal measure The individual ergodic theorem Gibbs' picture: mixing systems The definition of a mixing system Distribution functions for mixing systems Chaos The Green--Kubo formulae Linear response theory van Kampen's objections The Green--Kubo formula: diffusion The baker's transformation The transformation and its properties A model Boltzmann equation Bernoulli sequences Lyapunov exponents, baker's map, and toral automorphisms Definition of Lyapunov exponents The baker's transformation is ergodic The baker's transformation and irreversibility The Arnold cat map Kolmogorov--Sinai entropy Heuristic considerations The definition of the KS entropy Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem The Frobenius--Perron equation One-dimensional systems The Frobenius--Perron equation in higher dimensions Open systems and escape rates The escape-rate formalism The Smale horseshoe |
| ctrlnum | (ZDB-20-CBO)CR9780511628870 (OCoLC)849892654 (DE-599)BVBBV043941990 |
| dewey-full | 530.13/01/1857 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13/01/1857 |
| dewey-search | 530.13/01/1857 |
| dewey-sort | 3530.13 11 41857 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1017/CBO9780511628870 |
| format | Electronic eBook |
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| id | DE-604.BV043941990 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511628870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350960 |
| oclc_num | 849892654 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 287 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge lecture notes in physics |
| spelling | Dorfman, J. Robert 1937- Verfasser aut An introduction to chaos in nonequilibrium statistical mechanics J.R. Dorfman Cambridge Cambridge University Press 1999 1 online resource (xiv, 287 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge lecture notes in physics 14 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Nonequilibrium statistical mechanics The law of large numbers and the laws of mechanics Boltzmann's ergodic hypothesis Gibbs' mixing hypothesis Irregular dynamical motions Modern nonequilibrium statistical mechanics Outline of this book The Boltzmann equation Heuristic derivation Boltzmann's H-theorem Kac's ring model Tagged particle diffusion Liouville's equation Derivation The BBGKY hierarchy equations Poincare recurrence theorem Boltzmann's ergodic hypothesis Equal times in regions of equal measure The individual ergodic theorem Gibbs' picture: mixing systems The definition of a mixing system Distribution functions for mixing systems Chaos The Green--Kubo formulae Linear response theory van Kampen's objections The Green--Kubo formula: diffusion The baker's transformation The transformation and its properties A model Boltzmann equation Bernoulli sequences Lyapunov exponents, baker's map, and toral automorphisms Definition of Lyapunov exponents The baker's transformation is ergodic The baker's transformation and irreversibility The Arnold cat map Kolmogorov--Sinai entropy Heuristic considerations The definition of the KS entropy Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem The Frobenius--Perron equation One-dimensional systems The Frobenius--Perron equation in higher dimensions Open systems and escape rates The escape-rate formalism The Smale horseshoe 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 Nonequilibrium statistical mechanics Chaotic behavior in systems Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 s Chaostheorie (DE-588)4009754-7 s 1\p DE-604 Statistische Mechanik (DE-588)4056999-8 s 2\p DE-604 Chaotisches System (DE-588)4316104-2 s 3\p DE-604 Erscheint auch als Druckausgabe 978-0-521-65589-7 https://doi.org/10.1017/CBO9780511628870 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dorfman, J. Robert 1937- An introduction to chaos in nonequilibrium statistical mechanics Nonequilibrium statistical mechanics The law of large numbers and the laws of mechanics Boltzmann's ergodic hypothesis Gibbs' mixing hypothesis Irregular dynamical motions Modern nonequilibrium statistical mechanics Outline of this book The Boltzmann equation Heuristic derivation Boltzmann's H-theorem Kac's ring model Tagged particle diffusion Liouville's equation Derivation The BBGKY hierarchy equations Poincare recurrence theorem Equal times in regions of equal measure The individual ergodic theorem Gibbs' picture: mixing systems The definition of a mixing system Distribution functions for mixing systems Chaos The Green--Kubo formulae Linear response theory van Kampen's objections The Green--Kubo formula: diffusion The baker's transformation The transformation and its properties A model Boltzmann equation Bernoulli sequences Lyapunov exponents, baker's map, and toral automorphisms Definition of Lyapunov exponents The baker's transformation is ergodic The baker's transformation and irreversibility The Arnold cat map Kolmogorov--Sinai entropy Heuristic considerations The definition of the KS entropy Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem The Frobenius--Perron equation One-dimensional systems The Frobenius--Perron equation in higher dimensions Open systems and escape rates The escape-rate formalism The Smale horseshoe Nonequilibrium statistical mechanics Chaotic behavior in systems Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Chaostheorie (DE-588)4009754-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4136220-2 (DE-588)4009754-7 (DE-588)4056999-8 (DE-588)4316104-2 |
| title | An introduction to chaos in nonequilibrium statistical mechanics |
| title_alt | Nonequilibrium statistical mechanics The law of large numbers and the laws of mechanics Boltzmann's ergodic hypothesis Gibbs' mixing hypothesis Irregular dynamical motions Modern nonequilibrium statistical mechanics Outline of this book The Boltzmann equation Heuristic derivation Boltzmann's H-theorem Kac's ring model Tagged particle diffusion Liouville's equation Derivation The BBGKY hierarchy equations Poincare recurrence theorem Equal times in regions of equal measure The individual ergodic theorem Gibbs' picture: mixing systems The definition of a mixing system Distribution functions for mixing systems Chaos The Green--Kubo formulae Linear response theory van Kampen's objections The Green--Kubo formula: diffusion The baker's transformation The transformation and its properties A model Boltzmann equation Bernoulli sequences Lyapunov exponents, baker's map, and toral automorphisms Definition of Lyapunov exponents The baker's transformation is ergodic The baker's transformation and irreversibility The Arnold cat map Kolmogorov--Sinai entropy Heuristic considerations The definition of the KS entropy Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem The Frobenius--Perron equation One-dimensional systems The Frobenius--Perron equation in higher dimensions Open systems and escape rates The escape-rate formalism The Smale horseshoe |
| title_auth | An introduction to chaos in nonequilibrium statistical mechanics |
| title_exact_search | An introduction to chaos in nonequilibrium statistical mechanics |
| title_full | An introduction to chaos in nonequilibrium statistical mechanics J.R. Dorfman |
| title_fullStr | An introduction to chaos in nonequilibrium statistical mechanics J.R. Dorfman |
| title_full_unstemmed | An introduction to chaos in nonequilibrium statistical mechanics J.R. Dorfman |
| title_short | An introduction to chaos in nonequilibrium statistical mechanics |
| title_sort | an introduction to chaos in nonequilibrium statistical mechanics |
| topic | Nonequilibrium statistical mechanics Chaotic behavior in systems Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Chaostheorie (DE-588)4009754-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Nonequilibrium statistical mechanics Chaotic behavior in systems Nichtgleichgewichtsstatistik Chaostheorie Statistische Mechanik Chaotisches System |
| url | https://doi.org/10.1017/CBO9780511628870 |
| work_keys_str_mv | AT dorfmanjrobert anintroductiontochaosinnonequilibriumstatisticalmechanics |