Statistical mechanics: a short treatise
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | Texts and monographs in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 339 S. graph. Darst. |
| ISBN: | 9783540648833 |
Internformat
MARC
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| 100 | 1 | |a Gallavotti, Giovanni |d 1941- |e Verfasser |0 (DE-588)120874636 |4 aut | |
| 245 | 1 | 0 | |a Statistical mechanics |b a short treatise |c Giovanni Gallavotti |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIV, 339 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Texts and monographs in physics | |
| 650 | 4 | |a Statistische Mechanik | |
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Datensatz im Suchindex
| _version_ | 1828843349823455232 |
|---|---|
| adam_text |
GIOVANNI GALLAVOTTI
STATISTICAL MECHANICS
A
SHORT TREATISE
WITH 21 FIGURES
SPRINGER
TABLE OF CONTENTS
1.
CLASSICAL STATISTICAL MECHANICS
1
1.1
INTRODUCTION
1
1.2
MICROSCOPIC DYNAMICS
3
1.3
TIME AVERAGES
AND THE
ERGODIC HYPOTHESIS
10
1.4
RECURRENCE TIMES
AND
MACROSCOPIC OBSERVABLES
14
1.5
STATISTICAL ENSEMBLES
OR
"MONODES"
AND
MODELS
OF
THERMODYNAMICS. THERMODYNAMICS WITHOUT DYNAMICS
. 17
1.6
MODELS
OF
THERMODYNAMICS. MICROCANONICAL
AND
CANONICAL
ENSEMBLES
AND THE
ERGODIC HYPOTHESIS
20
1.7
CRITIQUE
OF THE
ERGODIC HYPOTHESIS
24
1.8
APPROACH
TO
EQUILIBRIUM
AND
BOLTZRNANN'S EQUATION.
ERGODICITY
AND
IRREVERSIBILITY
27
1.9 A
HISTORICAL NOTE.
THE
ETYMOLOGY
OF THE
WORD "ERGODIC"
AND
THE
HEAT THEOREMS
36
APPENDIX
1.A1
MONOCYCLIC SYSTEMS, KEPLERIAN MOTIONS
AND
ERGODIC HYPOTHESIS
44
APPENDIX
1.A2
GRAD-BOLTZMANN LIMIT
AND
LORENTZ'S
GAS 48
2.
STATISTICAL ENSEMBLES
57
2.1 STATISTICAL ENSEMBLES
AS
MODELS
OF
THERMODYNAMICS
57
2.2
CANONICAL
AND
MICROCANONICAL ENSEMBLES: ORTHODICITY
60
2.3
EQUIVALENCE BETWEEN CANONICAL
AND
MICROCANONICAL ENSEMBLES
68
2.4 NON-EQUIVALENCE
OF THE
CANONICAL
AND
MICROCANONICAL
ENSEMBLES.
PHASE TRANSITIONS. BOLTZMANN'S CONSTANT
73
2.5
THE
GRAND CANONICAL ENSEMBLE
AND
OTHER ORTHODIC ENSEMBLES
76
2.6 SOME TECHNICAL ASPECTS
84
3.
EQUIPARTITION
AND
CRITIQUE
89
3.1
EQUIPARTITION
AND
OTHER PARADOXES
AND
APPLICATIONS
OF
STATISTICAL MECHANICS
89
3.2 CLASSICAL STATISTICAL MECHANICS
WHEN
CELL SIZES
ARE NOT
NEGLIGIBLE
95
XII TABLE OF CONTENTS
3.3 INTRODUCTION TO QUANTUM STATISTICAL MECHANICS 103
3.4 PHILOSOPHICAL OUTLOOK ON THE FOUNDATIONS
OF
STATISTICAL MECHANICS 107
4.
THERMODYNAMIC LIMIT AND STABILITY
ILL
4.1
THE MEANING OF THE STABILITY CONDITIONS ILL
4.2 STABILITY CRITERIA 114
4.3 THERMODYNAMIC LIMIT 117
5. PHASE TRANSITIONS
129
5.1 VIRIAL THEOREM, VIRIAL SERIES AND VAN DER WAALS EQUATION . 129
5.2
THE MODERN INTERPRETATION
OF
VAN DER WAALS' APPROXIMATION 136
5.3 WHY A THERMODYNAMIC FORMALISM? 142
5.4 PHASE SPACE IN INFINITE VOLUME
AND
PROBABILITY DISTRIBUTIONS ON IT. GIBBS DISTRIBUTIONS . . 144
5.5
VARIATIONAL CHARACTERIZATION
OF
TRANSLATION INVARIANT GIBBS DISTRIBUTIONS 147
5.6 OTHER CHARACTERIZATIONS OF GIBBS DISTRIBUTIONS.
THE
DLR EQUATIONS 153
5.7 GIBBS DISTRIBUTIONS AND STOCHASTIC PROCESSES 155
5.8 ABSENCE OF PHASE TRANSITIONS:
D =
1. SYMMETRIES:
D =
2 .
157
5.9
ABSENCE OF PHASE TRANSITIONS: HIGH TEMPERATURE
AND
THE KS EQUATIONS 161
5.10 PHASE TRANSITIONS AND MODELS 167
APPENDIX 5.A1 ABSENCE OF PHASE TRANSITION
IN
NON-NEAREST-NEIGHBOR ONE-DIMENSIONAL SYSTEMS 172
6.
COEXISTENCE
OF
PHASES
175
6.1 THE ISING MODEL. INEQUIVALENCE OF CANONICAL
AND
GRAND CANONICAL ENSEMBLES 175
6.2 THE MODEL. GRAND CANONICAL AND CANONICAL ENSEMBLES.
THEIR
INEQUIVALENCE 176
6.3 BOUNDARY CONDITIONS. EQUILIBRIUM STATES 178
6.4 THE ISING MODEL IN ONE AND TWO DIMENSIONS
AND
ZERO FIELD 180
6.5 PHASE TRANSITIONS. DEFINITIONS 182
6.6 GEOMETRIC DESCRIPTION OF THE SPIN CONFIGURATIONS 184
6.7
PHASE TRANSITIONS. EXISTENCE 188
6.8 MICROSCOPIC DESCRIPTION OF THE PURE PHASES 189
6.9 RESULTS ON PHASE TRANSITIONS IN A WIDER RANGE
OF
TEMPERATURE 192
6.10 SEPARATION AND COEXISTENCE OF PURE PHASES.
PHENOMENOLOGICAL
CONSIDERATIONS 196
TABLE OF CONTENTS XIII
6.11 SEPARATION AND COEXISTENCE OF PHASES. RESULTS 198
6.12
SURFACE TENSION IN TWO DIMENSIONS.
ALTERNATIVE
DESCRIPTION OF THE SEPARATION PHENOMENA 199
6.13
THE STRUCTURE OF THE LINE OF SEPARATION.
WHAT A STRAIGHT LINE REALLY IS 200
6.14 PHASE SEPARATION PHENOMENA AND BOUNDARY CONDITIONS.
FURTHER
RESULTS 202
6.15 FURTHER RESULTS, SOME COMMENTS
AND
SOME OPEN PROBLEMS 205
7. EXACTLY SOLUBLE MODELS
209
7.1 TRANSFER MATRIX IN THE ISING MODEL: RESULTS IN
D =
1,
2
209
7.2
MEANING OF EXACT SOLUBILITY
AND
THE TWO-DIMENSIONAL ISING MODEL 211
7.3 VERTEX MODELS 214
7.4 A NONTRIVIAL EXAMPLE OF EXACT SOLUTION:
THE
TWO-DIMENSIONAL ISING MODEL 221
7.5 THE SIX-VERTEX MODEL AND BETHE'S ANSATZ 227
8. BROWNIAN MOTION
233
8.1 BROWNIAN MOTION AND EINSTEIN'S THEORY 233
8.2 SMOLUCHOWSKI'S THEORY 239
8.3 THE UHLENBECK-ORNSTEIN THEORY 242
8.4 WIENER'S THEORY 246
9. COARSE GRAINING AND NONEQUILIBRIUM
253
9.1
ERGODIC HYPOTHESIS REVISITED 253
9.2 TIMED OBSERVATIONS AND DISCRETE TIME 257
9.3 CHAOTIC HYPOTHESIS. ANOSOV SYSTEMS 260
9.4 KINEMATICS OF CHAOTIC MOTIONS. ANOSOV SYSTEMS . 265
9.5
SYMBOLIC DYNAMICS AND CHAOS 270
9.6 STATISTICS OF CHAOTIC ATTRACTORS. SRB DISTRIBUTIONS 278
9.7
ENTROPY GENERATION. TIME REVERSIBILITY
AND
FLUCTUATION THEOREM. EXPERIMENTAL TESTS
OF
THE CHAOTIC HYPOTHESIS 281
9.8 FLUCTUATION PATTERNS 287
9.9 "CONDITIONAL REVERSIBILITY" AND "FLUCTUATION THEOREMS" . . 288
9.10
ONSAGER RECIPROCITY AND GREEN-KUBO'S FORMULA 292
9.11
REVERSIBLE VERSUS IRREVERSIBLE DISSIPATION.
NONEQUILIBRIUM
ENSEMBLES? 294
APPENDIX 9.A1 MECANIQUE STATISTIQUE HORS EQUILIBRE:
L'HERITAGE
DE BOLTZMANN .; 298
APPENDIX 9.A2 HEURISTIC DERIVATION OF THE SRB DISTRIBUTION . . . 308
XIV TABLE OF CONTENTS
APPENDIX 9.A3 APERIODIC MOTIONS CAN BE REGARDED
AS
PERIODIC WITH INFINITE PERIOD! 310
APPENDIX 9.A4 GAUSS' LEAST CONSTRAINT PRINCIPLE 311
BIBLIOGRAPHY
313
NAME INDEX
331
SUBJECT INDEX
333 |
| any_adam_object | 1 |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-04-08T14:02:09Z |
| institution | BVB |
| isbn | 9783540648833 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008532718 |
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| physical | XIV, 339 S. graph. Darst. |
| publishDate | 1999 |
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| series2 | Texts and monographs in physics |
| spelling | Gallavotti, Giovanni 1941- Verfasser (DE-588)120874636 aut Statistical mechanics a short treatise Giovanni Gallavotti Berlin [u.a.] Springer 1999 XIV, 339 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Statistische Mechanik Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-662-03952-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallavotti, Giovanni 1941- Statistical mechanics a short treatise Statistische Mechanik Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 |
| title | Statistical mechanics a short treatise |
| title_auth | Statistical mechanics a short treatise |
| title_exact_search | Statistical mechanics a short treatise |
| title_full | Statistical mechanics a short treatise Giovanni Gallavotti |
| title_fullStr | Statistical mechanics a short treatise Giovanni Gallavotti |
| title_full_unstemmed | Statistical mechanics a short treatise Giovanni Gallavotti |
| title_short | Statistical mechanics |
| title_sort | statistical mechanics a short treatise |
| title_sub | a short treatise |
| topic | Statistische Mechanik Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistische Mechanik Statistical mechanics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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