Statistical dynamics: matter out of equilibrium
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke. |
| Physical Description: | VIII, 330 S. Ill., graph. Darst. |
| ISBN: | 1860940455 1860940463 |
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MARC
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| 100 | 1 | |a Bălescu, Radu |d 1932-2006 |e Verfasser |0 (DE-588)133965104 |4 aut | |
| 245 | 1 | 0 | |a Statistical dynamics |b matter out of equilibrium |c Radu Balescu |
| 264 | 1 | |a London |b Imperial College Press |c 1997 | |
| 300 | |a VIII, 330 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke. | ||
| 650 | 7 | |a Dynamica |2 gtt | |
| 650 | 7 | |a Statistische mechanica |2 gtt | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Dynamik |0 (DE-588)4013384-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtgleichgewichtsstatistik |0 (DE-588)4136220-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804126044232351744 |
|---|---|
| adam_text | Contents
Introduction
1
1.1
Bibliographical
Notes
BNI
........................ 5
States,
Dynamical Functions,
Evolution
7
2.1
General
Considerations..........................
7
2.2
Macroscopic Dynamical Systems
..................... 8
2.3
Microscopic Dynamical Systems
..................... 11
2.4
Systems of Interacting Particles
..................... 15
2.5
Bibliographical Notes BN2
........................ 20
General Formalism of Statistical Mechanics
21
3.1
Macroscopic Physics and Microscopic Physics
............. 21
3.2
The Phase Space Distribution Function
................. 23
3.3
Equilibrium States
............................ 29
3.4
Bibliographical Notes BN3
........................ 32
Reduced Distribution Functions and Correlation Functions
35
4.1
Classification of Dynamical Functions
.................. 35
4.2
Reduced Distribution Functions
..................... 37
4.3
Evolution of the Reduced Distribution Functions
............ 42
4.4
Correlation Functions
........................... 47
4.5
Evolution of the Correlation Functions
................. 49
4.6
Bibliographical Notes BN4
........................ 52
The Mean Field Approximation
55
5.1
Weakly Coupled Systems
......................... 55
5.2
Free Particle Dynamics
.......................... 59
5.3
The
Vlasov
Equation
........................... 60
5.4
The Linearized
Vlasov
Equation
..................... 65
5.5
Conclusions.
................................ 70
5.6
Bibliographical Notes BN5
........................ 71
vi
CONTENTS
6
The Weak Coupling Kinetic Equation
73
6.1
The Master Equation
........................... 73
6.2
The Landau Equation
.......................... 75
6.3
Explicit form of the Landau collision
tenn
............... 81
6.4
Conclusion
................................. 84
6.5
Appendix. The Cauchy Integral
..................... 84
6.6
Bibliographical Notes BN6
........................ 87
7
Kinetic Equation for Dilute Gases
89
7.1
The Dilute Gas Ordering
......................... 89
7.2
The Boltzmann Equation
......................... 90
7.3
Implementation of the Boltzmann Equation
.............. 97
7.4
Bibliographical Notes BN7
........................ 101
8
Kinetic Equation for Plasmas
105
8.1
The Plasma Ordering
........................... 105
8.2
The Integral Equation for the Correlation
............... 109
8.3
The Plasma Kinetic Equation
...................... 112
8.4
Properties of the Balescu-Lenard Equation
............... 116
8.5
Bibliographical Notes BN8
........................ 118
9
Properties of Kinetic Equations
121
9.1
The Concept of a Kinetic Equation
................... 121
9.2
Stochastic Equations of Evolution
.................... 123
9.3
Nature of the Collision Process
..................... 129
9.4
Irreversibility and Entropy
........................ 136
9.5
Spatially Inhomogeneous Systems
.................... 142
9.6
The Collisional Invariants
........................ 146
9.7
Bibliographical Notes BN9
........................ 148
10
Hydrodynamics and Transport
151
10.1
The Hydrodynamic Quantities
...................... 151
10.2
The Hydrodynamical Balance Equations
................ 154
10.3
Diffusion and Heat Conduction
..................... 156
10.4
The Hennitian Moment Expansion
................... 159
10.5
Derivation of the Transport Equations
................. 164
10.6
Properties of the Transport Coefficients
................. 167
10.7
Entropy and Transport
.......................... 170
10.8
Conclusions
................................ 174
10.9
Bibliographical Notes BN10
....................... 174
CONTENTS
vii
11 Transport
and Autocorrelation Functions
177
11.1
Introduction
................................ 177
11.2
Mean Square Displacement and Diffusion
................ 177
11.3
The
Langevin
Equations
......................... 180
11.4
The Hybrid Kinetic Equation
...................... 188
11.5
The Green-Kubo Formulae
........................ 193
11.6
Bibliographical Notes BN11
....................... 197
12
Random Walks and Transport
199
12.1
Classical Random Walks
......................... 199
12.2
Continuous Time Random Walks (CTRW)
............... 206
12.3
The Standard Long-Tail CTRW (SLT-CTRW)
............. 211
12.4
SLT-CTRW: The Density Profile
.................... 213
12.5
SLT-CTRW: The Non-Markovian Diffusion Equation
.......... 215
12.6
Markovian vs. Non-Markovian Evolution
................ 221
12.7
Appendix. Stable Probability Distribution Functions
......... 226
12.8
Bibliographical Notes BN12
....................... 228
13
Critical Phenomena
231
13.1
Overview of the Equilibrium Critical Phenomena
........... 231
13.2
Percolation
................................ 234
13.3
One-dimensional Systems
......................... 238
13.4
Scaling Theory of Percolation
...................... 240
13.5
Percolation Clusters and Fractals
.................... 245
13.6
Bibliographical Notes BN13
....................... 248
14
Transport on Percolation Structures
251
14.1
Electrical Conductivity and Percolation
................. 251
14.2
Diffusion and Percolation
......................... 254
14.3
Strange Diffusion on the Infinite Cluster
................ 258
14.4
Conclusions
................................ 265
14.5
Bibliographical Notes BN14
....................... 266
15
Chaos and Transport
269
15.1
The Standard Map
............................ 269
15.2
The Perron-Frobenius Operator
..................... 278
15.3
The Diffusive Regime
........................... 285
15.4
The
Subdiffusive
Regime
.......................... 293
15.5
Appendix. Transformation of the Resolvent
............... 308
15.6
Bibliographical Notes BN15
....................... 311
viü CONTENTS
16
Conclusions
313
16.1
The Status
of Statistical Dynamics
................... 313
16.2
Toward a Grand Theory of Irreversibility
?............... 315
16.3
Stochastic Statistical Dynamics
.................... 321
16.4
Bibliographical Notes BN16
....................... 322
Index
325
|
| any_adam_object | 1 |
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| author_GND | (DE-588)133965104 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV011523581 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:11Z |
| institution | BVB |
| isbn | 1860940455 1860940463 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007755078 |
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| physical | VIII, 330 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Bălescu, Radu 1932-2006 Verfasser (DE-588)133965104 aut Statistical dynamics matter out of equilibrium Radu Balescu London Imperial College Press 1997 VIII, 330 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke. Dynamica gtt Statistische mechanica gtt Stochastic processes Dynamik (DE-588)4013384-9 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 s DE-604 Dynamik (DE-588)4013384-9 s Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007755078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bălescu, Radu 1932-2006 Statistical dynamics matter out of equilibrium Dynamica gtt Statistische mechanica gtt Stochastic processes Dynamik (DE-588)4013384-9 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| subject_GND | (DE-588)4013384-9 (DE-588)4136220-2 |
| title | Statistical dynamics matter out of equilibrium |
| title_auth | Statistical dynamics matter out of equilibrium |
| title_exact_search | Statistical dynamics matter out of equilibrium |
| title_full | Statistical dynamics matter out of equilibrium Radu Balescu |
| title_fullStr | Statistical dynamics matter out of equilibrium Radu Balescu |
| title_full_unstemmed | Statistical dynamics matter out of equilibrium Radu Balescu |
| title_short | Statistical dynamics |
| title_sort | statistical dynamics matter out of equilibrium |
| title_sub | matter out of equilibrium |
| topic | Dynamica gtt Statistische mechanica gtt Stochastic processes Dynamik (DE-588)4013384-9 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| topic_facet | Dynamica Statistische mechanica Stochastic processes Dynamik Nichtgleichgewichtsstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007755078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT balescuradu statisticaldynamicsmatteroutofequilibrium |