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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1999
|
| Series: | Cambridge lecture notes in physics
14 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiv, 287 pages) |
| ISBN: | 9780511628870 |
| DOI: | 10.1017/CBO9780511628870 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941990 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s1999 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511628870 |c Online |9 978-0-511-62887-0 | ||
| 024 | 7 | |a 10.1017/CBO9780511628870 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511628870 | ||
| 035 | |a (OCoLC)849892654 | ||
| 035 | |a (DE-599)BVBBV043941990 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 530.13/01/1857 |2 21 | |
| 084 | |a UG 2000 |0 (DE-625)145616: |2 rvk | ||
| 084 | |a UG 3500 |0 (DE-625)145626: |2 rvk | ||
| 084 | |a UG 3900 |0 (DE-625)145629: |2 rvk | ||
| 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 |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1999 | |
| 300 | |a 1 online resource (xiv, 287 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 |
| 520 | |a 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 | ||
| 650 | 4 | |a Nonequilibrium statistical mechanics | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 0 | 7 | |a Nichtgleichgewichtsstatistik |0 (DE-588)4136220-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtgleichgewichtsstatistik |0 (DE-588)4136220-2 |D s |
| 689 | 0 | 1 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Statistische Mechanik |0 (DE-588)4056999-8 |D s |
| 689 | 1 | 1 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtgleichgewichtsstatistik |0 (DE-588)4136220-2 |D s |
| 689 | 2 | 1 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-65589-7 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511628870 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350960 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511628870 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511628870 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Record in the Search Index
| _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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05172nmm a2200649zcb4500</leader><controlfield tag="001">BV043941990</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s1999 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511628870</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-62887-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511628870</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511628870</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)849892654</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941990</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.13/01/1857</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 2000</subfield><subfield code="0">(DE-625)145616:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3500</subfield><subfield code="0">(DE-625)145626:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3900</subfield><subfield code="0">(DE-625)145629:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dorfman, J. Robert</subfield><subfield code="d">1937-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An introduction to chaos in nonequilibrium statistical mechanics</subfield><subfield code="c">J.R. Dorfman</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiv, 287 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge lecture notes in physics</subfield><subfield code="v">14</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2="0"><subfield code="t">Nonequilibrium statistical mechanics</subfield><subfield code="t">The law of large numbers and the laws of mechanics</subfield><subfield code="t">Boltzmann's ergodic hypothesis</subfield><subfield code="t">Gibbs' mixing hypothesis</subfield><subfield code="t">Irregular dynamical motions</subfield><subfield code="t">Modern nonequilibrium statistical mechanics</subfield><subfield code="t">Outline of this book</subfield><subfield code="t">The Boltzmann equation</subfield><subfield code="t">Heuristic derivation</subfield><subfield code="t">Boltzmann's H-theorem</subfield><subfield code="t">Kac's ring model</subfield><subfield code="t">Tagged particle diffusion</subfield><subfield code="t">Liouville's equation</subfield><subfield code="t">Derivation</subfield><subfield code="t">The BBGKY hierarchy equations</subfield><subfield code="t">Poincare recurrence theorem</subfield><subfield code="t">Boltzmann's ergodic hypothesis</subfield><subfield code="t">Equal times in regions of equal measure</subfield><subfield code="t">The individual ergodic theorem</subfield><subfield code="t">Gibbs' picture: mixing systems</subfield><subfield code="t">The definition of a mixing system</subfield><subfield code="t">Distribution functions for mixing systems</subfield><subfield code="t">Chaos</subfield><subfield code="t">The Green--Kubo formulae</subfield><subfield code="t">Linear response theory</subfield><subfield code="t">van Kampen's objections</subfield><subfield code="t">The Green--Kubo formula: diffusion</subfield><subfield code="t">The baker's transformation</subfield><subfield code="t">The transformation and its properties</subfield><subfield code="t">A model Boltzmann equation</subfield><subfield code="t">Bernoulli sequences</subfield><subfield code="t">Lyapunov exponents, baker's map, and toral automorphisms</subfield><subfield code="t">Definition of Lyapunov exponents</subfield><subfield code="t">The baker's transformation is ergodic</subfield><subfield code="t">The baker's transformation and irreversibility</subfield><subfield code="t">The Arnold cat map</subfield><subfield code="t">Kolmogorov--Sinai entropy</subfield><subfield code="t">Heuristic considerations</subfield><subfield code="t">The definition of the KS entropy</subfield><subfield code="t">Anosov and hyperbolic systems, Markov partitions, and Pesin's theorem</subfield><subfield code="t">The Frobenius--Perron equation</subfield><subfield code="t">One-dimensional systems</subfield><subfield code="t">The Frobenius--Perron equation in higher dimensions</subfield><subfield code="t">Open systems and escape rates</subfield><subfield code="t">The escape-rate formalism</subfield><subfield code="t">The Smale horseshoe</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonequilibrium statistical mechanics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chaotic behavior in systems</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtgleichgewichtsstatistik</subfield><subfield code="0">(DE-588)4136220-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Chaostheorie</subfield><subfield code="0">(DE-588)4009754-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistische Mechanik</subfield><subfield code="0">(DE-588)4056999-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Chaotisches System</subfield><subfield code="0">(DE-588)4316104-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtgleichgewichtsstatistik</subfield><subfield code="0">(DE-588)4136220-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Chaostheorie</subfield><subfield code="0">(DE-588)4009754-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Statistische Mechanik</subfield><subfield code="0">(DE-588)4056999-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Chaostheorie</subfield><subfield code="0">(DE-588)4009754-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Nichtgleichgewichtsstatistik</subfield><subfield code="0">(DE-588)4136220-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Chaotisches System</subfield><subfield code="0">(DE-588)4316104-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-65589-7</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511628870</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350960</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511628870</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511628870</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| 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 |