Chaos, scattering and statistical mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
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| Ausgabe: | 1.pub. |
| Schriftenreihe: | Cambridge nonlinear science series
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 475 S. Ill., graph. Darst. |
| ISBN: | 0521395119 |
Internformat
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| 100 | 1 | |a Gaspard, Pierre |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Chaos, scattering and statistical mechanics |c Pierre Gaspard |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1998 | |
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Datensatz im Suchindex
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| adam_text | CHAOS, SCATTERING AND STATISTICAL MECHANICS PIERRE GASPARD UNIVERSITE
LIBRE DE BRUXELLES FACULTE DES SCIENCES CENTER FOR NONLINEAR PHENOMENA
AND COMPLEX SYSTEMS UNIVERSITY PRESS CONTENTS PREFACE XVII INTRODUCTION
1 CHAPTER 1 DYNAMICAL SYSTEMS AND THEIR LINEAR STABILITY 12 1.1 *
DYNAMICS IN PHASE SPACE 12 1.1.1 THE GROUP OF TIME EVOLUTIONS 12 1.1.2
THE POINCARE MAP 13 1.1.3 HAMILTONIAN SYSTEMS 14 1.1.4 BILLIARDS 15
1.2 LINEAR STABILITY AND THE TANGENT SPACE I5 1.2.1 THE FUNDAMENTAL
MATRIX 15 1.2.2 LYAPUNOV EXPONENTS 16 1.2.3 DECOMPOSITION OF THE TANGENT
SPACE INTO ORTHOGONAL DIRECTIONS 17 1.2.4 HOMOLOGICAL DECOMPOSITION OF
THE MULTIPLICATIVE COCYCLE 19 1.2.5 THE LOCAL STRETCHING RATES 20 1.2.6
STABLE AND UNSTABLE MANIFOLDS 22 1.3 LINEAR STABILITY OF HAMILTONIAN
SYSTEMS 23 1.3.1 SYMPLECTIC DYNAMICS AND THE PAIRING RULE OF THE
LYAPUNOV EXPONENTS 23 1.3.2 VANISHING LYAPUNOV EXPONENTS AND THE LIE
GROUP OF CONTINUOUS SYMMETRIES 23 1.3.3 HAMILTON-JACOBI EQUATION AND THE
CURVATURE OF THE WAVEFRONT 25 VN VIII CONTENTS 1.3.4 ELIMINATION OF THE
NEUTRAL DIRECTIONS 28 1.3.5 THE LOCAL STRETCHING RATE IN F = 2
HYPERBOLIC HAMILTONIAN SYSTEMS 29 1.4 LINEAR STABILITY IN BILLIARDS 31
1.4.1 SOME DEFINITIONS 32 1.4.2 THE SECOND FUNDAMENTAL FORM 33 1.4.3 THE
TANGENT SPACE OF THE BILLIARD 33 1.4.4 FREE FLIGHT 34 1.4.5 COLLISION 35
1.4.6 EXPANDING AND CONTRACTING HOROSPHERES 36 1.4.7 TWO-DIMENSIONAL
HARD-DISK BILLIARDS (/ = 2) 39 CHAPTER 2 TOPOLOGICAL CHAOS 43 2.1
TOPOLOGY OF TRAJECTORIES IN PHASE SPACE 43 2.1.1 PHASE PORTRAIT AND
INVARIANT SET 43 2.1.2 CRITICAL ORBITS: STATIONARY POINTS , AND PERIODIC
ORBITS 44 2.1.3 NONWANDERING SETS 44 2.1.4 LOCALLY MAXIMAL INVARIANT
SETS AND GLOBAL STABILITY 45 2.1.5 DENSE ORBITS AND TRANSITIVITY 46
2.1.6 ATTRACTORS, ANTI-ATTRACTORS, AND REPELLERS 46 2.2 HYPERBOLICITY
47- 2.2.1 DEFINITION 47 2.2.2 ESCAPE-TIME FUNCTIONS 49 2.2.3 ANOSOV AND
AXIOM-A SYSTEMS 50 2.3 MARKOV PARTITION AND SYMBOLIC DYNAMICS IN
HYPERBOLIC SYSTEMS 52 2.3.1 PARTITIONING PHASE SPACE WITH STABLE AND
UNSTABLE MANIFOLDS 52 2.3.2 SYMBOLIC DYNAMICS AND SHIFT 53 ., 2.3.3
MARKOV TOPOLOGICAL SHIFT 55 2.4 TOPOLOGICAL ENTROPY 57 2.4.1 NETS AND
SEPARATED SUBSETS 58 2.4.2 DEFINITION AND PROPERTIES 58 2.5 THE SPECTRUM
OF PERIODIC ORBITS 60 2.5.1 PERIODIC ORBITS AND THE TOPOLOGICAL ZETA
FUNCTION 60 2.5.2 PRIME PERIODIC ORBITS AND FIXED POINTS 61 2.5.3 HOW TO
ORDER A SUM OVER PERIODIC ORBITS? 63 2.5.4 THE TOPOLOGICAL ENTROPY OF A
HYPERBOLIC INVARIANT SET 64 2.6 THE TOPOLOGICAL ZETA FUNCTION OF
HYPERBOLIC SYSTEMS 64 CONTENTS IX 2.6.1 THE TOPOLOGICAL ZETA FUNCTION
FOR A NONOVERLAPPING PARTITION 65 2.6.2 THE TOPOLOGICAL ZETA FUNCTION
FOR AN OVERLAPPING PARTITION 65 CHAPTER 3 IIOUVILLIAN DYNAMICS 67 3.1
STATISTICAL ENSEMBLES 67 3.2 TIME EVOLUTION OF STATISTICAL ENSEMBLES 68
3.2.1 LIOUVILLE EQUATION 68 3.2.2 FROBENIUS-PERRON AND KOOPMAN OPERATORS
69 3.2.3 BOUNDARY CONDITIONS 70 3.3 INVARIANT MEASURES 72 3.3.1
DEFINITION 72 3.3.2 SELECTION OF AN INVARIANT MEASURE 73 3.3.3 THE BASIC
INVARIANT MEASURES OF HAMILTONIAN SYSTEMS 74 3.4 CORRELATION FUNCTIONS
AND SPECTRAL FUNCTIONS 75 3.5 SPECTRAL THEORY ON REAL FREQUENCIES 76
3.5.1 SPECTRAL DECOMPOSITION ON A HILBERT SPACE 76 3.5.2 PURELY DISCRETE
REAL SPECTRUM 77 3.5.3 CONTINUOUS REAL SPECTRUM 78 3.5.4 CONTINUOUS REAL
SPECTRUM AND THE WIENER-KHINCHIN THEOREM 81 3.5.5 CONTINUOUS REAL
SPECTRUM AND GAUSSIAN FLUCTUATIONS 82 3.6 SPECTRAL THEORY ON COMPLEX
FREQUENCIES OR RESONANCE * THEORY 83 3.6.1 ANALYTIC CONTINUATION TO
COMPLEX FREQUENCIES 83 3.6.2 SINGULARITIES AS A SPECTRUM OF GENERALIZED
EIGENVALUES 87 3.6.3 DEFINITION OF A TRACE 91 3.7 RESONANCES OF
STATIONARY POINTS 94 3.7.1 TRACE FORMULA AND EIGENVALUES 94 . 3.7.2
EIGENSTATES AND SPECTRAL DECOMPOSITIONS 96 3.7.3 HAMILTONIAN STATIONARY
POINT OF SADDLE TYPE 100 3.8 RESONANCES FOR HYPERBOLIC SETS WITH
PERIODIC ORBITS 103 3.8.1 TRACE FORMULA 103 3.8.2 THE SELBERG-SMALE ZETA
FUNCTION 105 3.8.3 FORMULATION OF THE EIGENVALUE PROBLEM 110 3.8.4
FREDHOLM DETERMINANT 113 3.8.5 FREDHOLM THEORY FOR THE EIGENSTATES 114
3.8.6 PERIODIC-ORBIT AVERAGES OF OBSERVABLES 116 3.9 RESONANCE SPECTRUM
AT BIFURCATIONS 118 CONTENTS 3.9.1 PITCHFORK BIFURCATION 119 3.9.2
HOPFBIFURCATION 120 3.9.3 HOMOCLINIC BIFURCATION IN A TWO-DIMENSIONAL
FLOW 122 3.10 LIOUVILLIAN DYNAMICS OF ONE-DIMENSIONAL MAPS 123 CHAPTER 4
PROBABILISTIC CHAOS 126 4.1 DYNAMICAL RANDOMNESS AND THE ENTROPY PER
UNIT TIME 126 4.1.1 A MODEL OF OBSERVATION 127 4.1.2 INFORMATION
REDUNDANCY AND ALGORITHMIC COMPLEXITY 128 4.1.3 KOLMOGOROV-SINAI ENTROPY
PER UNIT TIME 130 4.2 THE LARGE-DEVIATION FORMALISM 131 4.2.1 SEPARATED
SUBSETS 132 4.2.2 TOPOLOGICAL PRESSURE AND THE DYNAMICAL INVARIANT
MEASURES 132 4.2.3 PRESSURE FUNCTIONS BASED ON THE LYAPUNOV EXPONENTS
135 4.2.4 ENTROPY FUNCTION AND LEGENDRE TRANSFORM 136 4.3 CLOSED
HYPERBOLIC SYSTEMS 138 4.3.1 THE MICROCANONICAL MEASURE AS A
SINAI-RUELLE-BOWEN DYNAMICAL MEASURE 138 4.3.2 THE PRESSURE FUNCTION FOR
CLOSED SYSTEMS 140 4.3.3 GENERATING FUNCTIONS OF OBSERVABLES AND
TRANSPORT COEFFICIENTS 141 4.4 OPEN HYPERBOLIC SYSTEMS 142 .. 4.4.1 THE
NONEQUILIBRIUM INVARIANT MEASURE OF THE REPELLER 143 4.4.2 CONNECTION
WITH THE DYNAMICAL INVARIANT MEASURE AND THE PRESSURE FUNCTION 145 4.4.3
FRACTAL REPELLERS IN TWO-DEGREES-OF-FREEDOM SYSTEMS AND THEIR DIMENSIONS
148 4.5 GENERALIZED ZETA FUNCTIONS 152 4.5.1 FRQBENIUS-PERRON OPERATORS
IN THE LARGE-DEVIATION FORMALISM 152 4.5.2 THE TOPOLOGICAL PRESSURE AS
AN EIGENVALUE 154 4.6 PROBABILISTIC MARKOV CHAINS AND LATTICE GAS
AUTOMATA 156 4.6.1 MARKOV CHAIN MODELS 156 4.6.2 ISOMORPHISM BETWEEN
MARKOV CHAINS AND AREA-PRESERVING MAPS 157 4.6.3 REPELLERS OF MARKOV
CHAINS 159 4.6.4 LARGE-DEVIATION FORMALISM OF MARKOV CHAINS 161 CONTENTS
XI 4.7 SPECIAL FRACTALS GENERATED BY UNIFORMLY HYPERBOLIC MAPS 163 4.7.1
CONDITION ON THE MEAN SOJOURN TIME IN A DOMAIN 163 4.7.2 FRACTAL
REPELLER GENERATED IN TRAJECTORY RECONSTRUCTION 167 4.8 NONHYPERBOLIC
SYSTEMS 169 CHAPTER 5 CHAOTIC SCATTERING 171 5.1 CLASSICAL SCATTERING
THEORY 171 5.1.1 MOTIVATIONS 171 5.1.2 CLASSICAL SCATTERING FUNCTION AND
TIME DELAY 172 5.1.3 THE DIFFERENT TYPES OF TRAJECTORIES 174 5.1.4
SCATTERING OPERATOR FOR STATISTICAL ENSEMBLES 176 5.2 HARD-DISK
SCATTERERS 176 5.2.1 GENERALITIES 176 5.2.2 THE DYNAMICS 177 5.2.3 THE
BIRKHOFF MAPPING 179 5.2.4 THE ONE-DISK SCATTERER 180 5.2.5 THE TWO-DISK
SCATTERER 181 5.2.6 THE THREE-DISK SCATTERER 183 5.2.7 THE FOUR-DISK
SCATTERER 201 5.3 HAMILTONIAN MAPPING OF SCATTERING TYPE 210 5.3.1
DEFINITION OF THE MODEL 210 5.3.2 METAMORPHOSES OF THE PHASE PORTRAITS
211 5.3.3 CHARACTERISTIC QUANTITIES OF THE CHAOTIC REPELLER 215 . 5.4
APPLICATION TO THE MOLECULAR TRANSITION STATE 216 5.4.1 MODEL OF
PHOTODISSOCIATION OF HGH 216 5.4.2 TRANSITION FROM A PERIODIC TO A
CHAOTIC REPELLER 218 5.4.3 THREE-BRANCHED SMALE REPELLER AND ITS
CHARACTERIZATION 219 5.5 FURTHER APPLICATIONS OF CHAOTIC SCATTERING 221
CHAPTER 6 SCATTERING THEORY OF TRANSPORT 224 6.1 SCATTERING AND
TRANSPORT 224 6.2 DIFFUSION AND CHAOTIC SCATTERING 225 6.2.1 LARGE
SCATTERERS AND THE DIFFUSION EQUATION 225 6.2.2 ESCAPE-TIME FUNCTION AND
ESCAPE RATE 226 6.2.3 PHENOMENOLOGY OF THE ESCAPE PROCESS 229 6.2.4 THE
ESCAPE-RATE FORMULA FOR DIFFUSION 231 6.3 THE PERIODIC LORENTZ GAS 234
XII CONTENTS 6.3.1 DEFINITION 234 6.3.2 THE LIOUVILLE INVARIANT MEASURE
235 6.3.3 FINITE AND INFINITE HORIZONS 236 6.3.4 CHAOTIC PROPERTIES OF
THE INFINITE LORENTZ GAS 237 6.3.5 THE OPEN LORENTZ GAS 244 6.4 THE
MULTIBAKER MAPPING 250 6.4.1 DEFINITION 250 6.4.2 THE POLLICOTT-RUELLE
RESONANCES AND THE ESCAPE-RATE FORMULA 254 6.5 ESCAPE-RATE FORMALISM FOR
GENERAL TRANSPORT COEFFICIENTS 257 6.5.1 GENERAL CONTEXT 257 6.5.2
TRANSPORT COEFFICIENTS AND THEIR HELFAND MOMENTS 258 6.5.3
GENERALIZATION OF THE ESCAPE-RATE FORMULA 261 6.6 ESCAPE-RATE FORMALISM
FOR CHEMICAL REACTION RATES 264 6.6.1 NONEQUILIBRIUM THERMODYNAMICS OF
CHEMICAL REACTIONS 265 6.6.2 THE MASTER EQUATION APPROACH 266 6.7
DISCUSSION 268 6.7.1 SUMMARY 268 6.7.2 FURTHER APPLICATIONS OF THE
ESCAPE-RATE FORMALISM 269 6.7.3 RELATION TO THE THERMOSTATTED-SYSTEM
APPROACH 270 6.7.4 THE ESCAPE-RATE FORMALISM IN THE PRESENCE OF EXTERNAL
FORCES 272 CHAPTER 7 HYDRODYNAMIC MODES OF DIFFUSION 275 11
HYDRODYNAMICS FROM LIOUVILLIAH DYNAMICS 275 7.1.1 HISTORICAL BACKGROUND
AND MOTIVATION 275 7.1.2 POLLICOTT-RUELLE RESONANCES AND QUASIPERIODIC
BOUNDARY CONDITIONS 276 7.2 LIOUVILLIAN DYNAMICS FOR SYSTEMS SYMMETRIC
UNDER A GROUP OF SPATIAL TRANSLATIONS 278 7.2.1 INTRODUCTION 278 7.2.2
SUSPENDED FLOWS OF INFINITE SPATIAL EXTENSION 279 7.2.3 ASSUMPTIONS ON
THE PROPERTIES OF THE MAPPING 282 7.2.4 INVARIANT MEASURES 283 7.2.5
-TIME-REVERSAL SYMMETRY 284 7.2.6 THE FROBENIUS-PERRON OPERATOR ON THE
INFINITE LATTICE 284 7.2.7 SPATIAL FOURIER TRANSFORMS 285 7.2.8 THE
FROBENIUS-PERRON OPERATORS IN THE WAVENUMBER SUBSPACES 286 CONTENTS XLII
C 7.2.9 TIME-REVERSAL SYMMETRY FOR THE ^-COMPONENTS 288 7.2.10
REDUCTION TO THE FROBENIUS-PERRON OPERATOR OF THE MAPPING 289 7.2.11
EIGENVALUE PROBLEM AND ZETA FUNCTION 289 7.2.12 CONSEQUENCES OF
TIME-REVERSAL SYMMETRY ON THE RESONANCES 291 7.2.13 RELATION TO THE
EIGENVALUE PROBLEM FOR THE FLOW 292 7.3 DETERMINISTIC DIFFUSION 293
7.3.1 INTRODUCTION 293 7.3.2 MEAN DRIFT 294 7.3.3 THE FIRST DERIVATIVE
OF THE EIGENSTATE WITH RESPECT TO THE WAVENUMBER 295 7.3.4 DIFFUSION
MATRIX 296 7.3.5 HIGHER-ORDER DIFFUSION COEFFICIENTS 297 7.3.6
EIGENVALUES AND THE VAN HOVE FUNCTION 299 7.3.7 PERIODIC-ORBIT FORMULA
FOR THE DIFFUSION COEFFICIENT 302 7.3.8 CONSEQUENCES OF THE LATTICE
SYMMETRY UNDER A POINT GROUP 303 7.4 DETERMINISTIC DIFFUSION IN THE
PERIODIC LORENTZ GAS 305 7.4.1 PROPERTIES OF THE INFINITE LORENTZ GAS
305 7.4.2 DIFFUSION AND ITS DISPERSION RELATION 309 7.4.3 CUMULATIVE
FUNCTIONS OF THE EIGENSTATES 310 7.5 DETERMINISTIC DIFFUSION IN THE
PERIODIC MULTIBAKER 312 7.5.1 PROPERTIES OF THE PERIODIC MULTIBAKER
312 7.5.2 THE FROBENIUS-PERRON OPERATOR AND ITS POLLICOTT-RUELLE
RESONANCES 313 7.5.3 GENERALIZED SPECTRAL DECOMPOSITION 316 7.5.4
ANALYSIS OFTHE ASSOCIATED ONE-DIMENSIONAL MAP 318 7.5.5 THE ROOT STATES
OFTHE TWO-DIMENSIONAL MAP 326 7.6 EXTENSIONS TO THE OTHER TRANSPORT
PROCESSES 334 7.6.1 GAUSSIAN FLUCTUATIONS OF THE HELFAND MOMENTS 334
7.6.2 THE MINIMAL MODELS OF TRANSPORT 336 7.6.3 VISCOSITY AND
SELF-DIFFUSION IN TWO-PARTICLE FLUIDS 337 7.6.4 SPONTANEOUS SYMMETRY
BREAKING AND GOLDSTONE HYDRODYNAMIC MODES 339 7.7 CHEMIO-HYDRODYNAMIC
MODES 340 XIV CONTENTS CHAPTER 8 SYSTEMS MAINTAINED OUT OF EQUILIBRIUM
343 8.1 NONEQUILIBRIUM SYSTEMS IN LIOUVILLIAN DYNAMICS 343 8.2
NONEQUILIBRIUM STEADY STATES OF DIFFUSION 345 8.2.1 PHENOMENOLOGICAL
DESCRIPTION OF THE STEADY STATES 345 8.2.2 DETERMINISTIC DESCRIPTION OF
THE STEADY STATES 346 8.3 FROM THE HYDRODYNAMIC MODES TO THE
NONEQUILIBRIUM STEADY STATES 350 8.3.1 FROM THE EIGENSTATES TO THE
NONEQUILIBRIUM STEADY STATES 350 8.3.2 MICROSCOPIC CURRENT AND FICK S
LAW 352 8.3.3 NONEQUILIBRIUM STEADY STATES OF THE PERIODIC LORENTZ GAS
353 8.3.4 NONEQUILIBRIUM STEADY STATES OF THE PERIODIC MULTIBAKER 355
8.3.5 NONEQUILIBRIUM STEADY STATES OF THE LANGEVIN PROCESS 359 8.4 FROM
THE FINITE TO THE INFINITE MULTIBAKER 361 8.5 GENERALIZATION TO THE
OTHER TRANSPORT PROCESSES 366 8.6 ENTROPY PRODUCTION 368 8.6.1
IRREVERSIBLE THERMODYNAMICS AND THE PROBLEM OF ENTROPY PRODUCTION 370
8.6.2 COMPARISON WITH DETERMINISTIC SCHEMES 371 8.6.3 OPEN SYSTEMS AND
THEIR POISSON SUSPENSION 373 8.6.4 THE S-ENTROPY 376 8.6.5 ENTROPY
PRODUCTION IN THE MULTIBAKER MAP 378 8.6.6 SUMMARY 383 8.7 COMMENTS ON
FAR-FROM-EQUILIBRIUM SYSTEMS 385 CHAPTER 9 NOISES AS MICROSCOPIC CHAOS
387 9.1 DIFFERENCES AND SIMILARITIES BETWEEN NOISES AND CHAOS 387 9.2
(E, I)-ENTROPY PER UNIT TIME 390 9.2.1 DYNAMICAL PROCESSES 390 9.2.2
ENTROPY OF A PROCESS OVER A TIME INTERVAL T AND A PARTITION * 391 9.2.3
PARTITION (E,T)-ENTROPY PER UNIT TIME 392 9.2.4 COHEN-PROCACCIA (E,
X)-ENTROPY PER UNIT TIME 393 9.2.5 SHANNON-KOLMOGOROV {E, T)-ENTROPY PER
UNIT TIME 394 9.3 TIME RANDOM PROCESSES 397 9.3.1 DETERMINISTIC
PROCESSES 397 9.3.2 BERNOULLI AND MARKOV CHAINS 398 9.3.3
BIRTH-AND-DEATH PROCESSES 399 9.3.4 TIME-DISCRETE, AMPLITUDE-CONTINUOUS
RANDOM PROCESSES 402 CONTENTS XV 9.3.5 TIME- AND AMPLITUDE-CONTINUOUS
RANDOM PROCESSES 406 9.3.6 WHITE NOISE 411 9.3.7 LEVY FLIGHTS 411 -
9.3.8 CLASSIFICATION OF THE TIME RANDOM PROCESSES 412 9.4 SPACETIME
RANDOM PROCESSES 415 9.4.1 (E,X)-ENTROPY PER UNIT TIME AND VOLUME 415
9.4.2 DETERMINISTIC CELLULAR AUTOMATA 415 9.4.3 LATTICE GAS AUTOMATA 416
9.4.4 COUPLED MAP LATTICES 416 9.4.5 NONLINEAR PARTIAL DIFFERENTIAL
EQUATIONS 417 9.4.6 STOCHASTIC SPIN DYNAMICS 417 9.4.7 SPACETIME
GAUSSIAN FIELDS 417 9.4.8 SPORADIC SPACETIME RANDOM PROCESSES 418 9.4.9
CLASSIFICATION OF SPACETIME RANDOM PROCESSES 419 9.5 RANDOM PROCESSES OF
STATISTICAL MECHANICS 419 9.5.1 IDEAL GASES 420 9.5.2 THE LORENTZ GASES
AND THE HARD-SPHERE GASES 424 9.5.3 THE BOLTZMANN-LORENTZ PROCESS 425
9.6 BROWNIAN MOTION AND MICROSCOPIC CHAOS 429 9.6.1 HAMILTONIAN AND
LANGEVIN MODELS OF BROWNIAN MOTION 429 9.6.2 A LOWER BOUND ON THE
POSITIVE LYAPUNOV EXPONENTS 430 9.6.3 SOME CONCLUSIONS 431 CHAPTER 10
CONCLUSIONS AND PERSPECTIVES 433 10.1 OVERVIEW OF THE RESULTS 433 10.1.1
FROM DYNAMICAL INSTABILITY TO STATISTICAL ENSEMBLES 433 10.1.2 DYNAMICAL
CHAOS 438 10.1.3 FRACTAL REPELLERS AND CHAOTIC SCATTERING 441 10.1.4
SCATTERING THEORY OF TRANSPORT 442 10.1.5 RELAXATION TO EQUILIBRIUM 442
10.1.6 NONEQUILIBRIUM STEADY STATES AND ENTROPY PRODUCTION 447 10.1.7
IRREVERSIBILITY 448 10.1.8 POSSIBLE EXPERIMENTAL SUPPORT FOR THE
HYPOTHESIS OF MICROSCOPIC CHAOS 451 10.2 PERSPECTIVES AND OPEN QUESTIONS
452 10.2.1 EXTENSIONS TO GENERAL AND DISSIPATIVE DYNAMICAL SYSTEMS 453
XVI CONTENTS 10.2.2 EXTENSIONS IN NONEQUILIBRIUM STATISTICAL MECHANICS
454 10.2.3 EXTENSIONS TO QUANTUM-MECHANICAL SYSTEMS 456 REFERENCES 458
INDEX 471
|
| any_adam_object | 1 |
| author | Gaspard, Pierre |
| author_facet | Gaspard, Pierre |
| author_role | aut |
| author_sort | Gaspard, Pierre |
| author_variant | p g pg |
| building | Verbundindex |
| bvnumber | BV012082778 |
| classification_rvk | UG 3100 UG 3900 |
| classification_tum | MAT 587f PHY 063f PHY 057f |
| ctrlnum | (OCoLC)247489551 (DE-599)BVBBV012082778 |
| discipline | Physik Mathematik |
| edition | 1.pub. |
| format | Book |
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| genre | 1\p (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV012082778 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:21:23Z |
| institution | BVB |
| isbn | 0521395119 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008181065 |
| oclc_num | 247489551 |
| open_access_boolean | |
| owner | DE-20 DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM DE-29T DE-83 DE-11 DE-188 |
| physical | XIX, 475 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge nonlinear science series |
| series2 | Cambridge nonlinear science series |
| spelling | Gaspard, Pierre Verfasser aut Chaos, scattering and statistical mechanics Pierre Gaspard 1.pub. Cambridge [u.a.] Cambridge Univ. Press 1998 XIX, 475 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge nonlinear science series 9 Chaostheorie (DE-588)4009754-7 gnd rswk-swf Streuung (DE-588)4058056-8 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Transporttheorie (DE-588)4185936-4 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Chaotisches System (DE-588)4316104-2 s Streuung (DE-588)4058056-8 s DE-604 Nichtgleichgewichtsstatistik (DE-588)4136220-2 s Chaostheorie (DE-588)4009754-7 s Transporttheorie (DE-588)4185936-4 s Cambridge nonlinear science series 9 (DE-604)BV004573757 9 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008181065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gaspard, Pierre Chaos, scattering and statistical mechanics Cambridge nonlinear science series Chaostheorie (DE-588)4009754-7 gnd Streuung (DE-588)4058056-8 gnd Chaotisches System (DE-588)4316104-2 gnd Transporttheorie (DE-588)4185936-4 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4058056-8 (DE-588)4316104-2 (DE-588)4185936-4 (DE-588)4136220-2 (DE-588)1071861417 |
| title | Chaos, scattering and statistical mechanics |
| title_auth | Chaos, scattering and statistical mechanics |
| title_exact_search | Chaos, scattering and statistical mechanics |
| title_full | Chaos, scattering and statistical mechanics Pierre Gaspard |
| title_fullStr | Chaos, scattering and statistical mechanics Pierre Gaspard |
| title_full_unstemmed | Chaos, scattering and statistical mechanics Pierre Gaspard |
| title_short | Chaos, scattering and statistical mechanics |
| title_sort | chaos scattering and statistical mechanics |
| topic | Chaostheorie (DE-588)4009754-7 gnd Streuung (DE-588)4058056-8 gnd Chaotisches System (DE-588)4316104-2 gnd Transporttheorie (DE-588)4185936-4 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd |
| topic_facet | Chaostheorie Streuung Chaotisches System Transporttheorie Nichtgleichgewichtsstatistik Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008181065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004573757 |
| work_keys_str_mv | AT gaspardpierre chaosscatteringandstatisticalmechanics |