Statistical physics: an advanced approach with applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIV, 553 S. graph. Darst. |
| ISBN: | 3642286836 9783642286834 9783642286841 |
Internformat
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
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IMAGE 1
CONTENTS
1 STATISTICAL PHYSICS: IS MORE THAN STATISTICAL MECHANICS 1
PART I MODELING O F STATISTICAL SYSTEMS
2 RANDOM VARIABLES: FUNDAMENTALS O F PROBABILITY THEORY AND STATISTICS 5
2.1 PROBABILITY AND RANDOM VARIABLES 6
2.1.1 THE SPACE OF EVENTS 6
2.1.2 INTRODUCTION O F PROBABILITY 7
2.1.3 RANDOM VARIABLES 9
2.2 MULTIVARIATE RANDOM VARIABLES AND CONDITIONAL PROBABILITIES 13 2.2.1
MULTIDIMENSIONAL RANDOM VARIABLES 13
2.2.2 MARGINAL DENSITIES 14
2.2.3 CONDITIONAL PROBABILITIES AND BAYES' THEOREM 14
2.3 MOMENTS AND QUANTILES 19
2.3.1 MOMENTS 19
2.3.2 QUANTILES 23
2.4 THE ENTROPY 2 5
2.4.1 ENTROPY FOR A DISCRETE SET O F EVENTS 25
2.4.2 ENTROPY FOR A CONTINUOUS SPACE O F EVENTS 2 6
2.4.3 RELATIVE ENTROPY 27
2.4.4 REMARKS 28
2.4.5 APPLICATIONS 28
2.5 COMPUTATIONS WITH RANDOM VARIABLES 32
2.5.1 ADDITION AND MULTIPLICATION O F RANDOM VARIABLES 32
2.5.2 FURTHER IMPORTANT RANDOM VARIABLES 36
2.5.3 LIMIT THEOREMS 38
2.6 STABLE RANDOM VARIABLES AND RENORMALIZATION TRANSFORMATIONS 4 0
2.6.1 STABLE RANDOM VARIABLES 41
2.6.2 THE RENORMALIZATION TRANSFORMATION 4 3
IX
HTTP://D-NB.INFO/1019655291
IMAGE 2
X C O N T E N T S
2.6.3 STABILITY ANALYSIS 44
2.6.4 SCALING BEHAVIOR 4 6
2.7 THE LARGE DEVIATION PROPERTY FOR SUMS OF RANDOM VARIABLES - 47
3 RANDOM VARIABLES IN STATE SPACE: CLASSICAL STATISTICAL MECHANICS O F
FLUIDS 53
3.1 THE MICROCANONICAL SYSTEM 54
3.2 SYSTEMS IN CONTACT 57
3.2.1 THERMAL CONTACT 57
3.2.2 SYSTEMS WITH EXCHANGE OF VOLUME AND ENERGY 65
3.2.3 SYSTEMS WITH EXCHANGE O F PARTICLES AND ENERGY 7 0
3.3 THERMODYNAMIC POTENTIALS 73
3.4 SUSCEPTIBILITIES 79
3.4.1 HEAT CAPACITIES 79
3.4.2 ISOTHERMAL COMPRESSIBILITY 81
3.4.3 ISOBARIC EXPANSIVITY 82
3.4.4 ISOCHORIC TENSION COEFFICIENT AND ADIABATIC COMPRESSIBILITY 83
3.4.5 A GENERAL RELATION BETWEEN RESPONSE FUNCTIONS 83
3.5 THE EQUIPARTITION THEOREM 85
3.6 THE RADIAL DISTRIBUTION FUNCTION 87
3.7 APPROXIMATION METHODS 9 4
3.7.1 THE VIRIAL EXPANSION 94
3.7.2 INTEGRAL EQUATIONS FOR THE RADIAL DISTRIBUTION FUNCTION 102
3.7.3 PERTURBATION THEORY 104
3.8 THE VAN DER WAALS EQUATION 107
3.8.1 THE ISOTHERMS 108
3.8.2 THE MAXWELL CONSTRUCTION 110
3.8.3 CORRESPONDING STATES 112
3.8.4 CRITICAL EXPONENTS 114
3.9 SOME GENERAL REMARKS ABOUT PHASE TRANSITIONS AND PHASE DIAGRAMS 116
4 RANDOM FIELDS: TEXTURES AND CLASSICAL STATISTICAL MECHANICS O F SPIN
SYSTEMS 121
4.1 DISCRETE STOCHASTIC FIELDS 122
4.1.1 MARKOV FIELDS 123
4.1.2 GIBBS FIELDS 125
4.1.3 EQUIVALENCE O F GIBBS AND MARKOV FIELDS 126
4.2 EXAMPLES O F MARKOV RANDOM FIELDS 127
4.2.1 MODEL WITH INDEPENDENT RANDOM VARIABLES 127
4.2.2 AUTO MODEL 128
4.2.3 MULTILEVEL LOGISTIC MODEL 129
4.2.4 GAUSS MODEL 130
IMAGE 3
CONTENTS XI
4.3 CHARACTERISTIC QUANTITIES O F DENSITIES FOR RANDOM FIELDS 130
4.4 SIMPLE RANDOM FIELDS 133
4.4.1 THE WHITE RANDOM FIELD OR THE IDEAL PARAMAGNETIC SYSTEM 133
4.4.2 THE ONE-DIMENSIONAL ISING MODEL 135
4.5 RANDOM FIELDS WITH PHASE TRANSITIONS 139
4.5.1 THE CURIE-WEISS MODEL 139
4.5.2 THE MEAN FIELD APPROXIMATION 141
4.5.3 THE TWO-DIMENSIONAL ISING MODEL 146
4.6 THE LANDAU FREE ENERGY 152
4.7 THE RENORMALIZATION GROUP METHOD FOR RANDOM FIELDS AND SCALING LAWS
155
4.7.1 THE RENORMALIZATION TRANSFORMATION 155
4.7.2 SCALING LAWS 156
5 TIME-DEPENDENT RANDOM VARIABLES: CLASSICAL STOCHASTIC PROCESSES 161
5.1 MARKOV PROCESSES 162
5.2 THE MASTER EQUATION 166
5.3 EXAMPLES OF MASTER EQUATIONS 172
5.3.1 ONE-STEP PROCESSES 172
5.3.2 CHEMICAL REACTIONS 175
5.3.3 REACTION-DIFFUSION SYSTEMS 176
5.3.4 SCATTERING PROCESSES 177
5.4 ANALYTIC SOLUTIONS OF MASTER EQUATIONS 178
5.4.1 EQUATIONS FOR THE MOMENTS 178
5.4.2 THE EQUATION FOR THE CHARACTERISTIC FUNCTION 179
5.4.3 EXAMPLES 180
5.5 SIMULATION O F STOCHASTIC PROCESSES AND FIELDS 183
5.6 THE FOKKER-PLANCK EQUATION 191
5.6.1 FOKKER-PLANCK EQUATION WITH LINEAR DRIFT TERM AND ADDITIVE NOISE
194
5.7 THE LINEAR RESPONSE FUNCTION AND THE FLUCTUATION- DISSIPATION
THEOREM 197
5.8 APPROXIMATION METHODS 200
5.8.1 THE 2 EXPANSION 201
5.8.2 THE ONE-PARTICLE PICTURE 207
5.9 MORE GENERAL STOCHASTIC PROCESSES 210
5.9.1 SELF-SIMILAR PROCESSES 210
5.9.2 FRACTAL BROWNIAN MOTION 211
5.9.3 STABLE LEVY PROCESSES 212
5.9.4 AUTOREGRESSIVE PROCESSES 213
IMAGE 4
XH C O N T E N T S
6 QUANTUM RANDOM SYSTEMS 221
6.1 QUANTUM-MECHANICAL DESCRIPTION O F STATISTICAL SYSTEMS 221
6.2 IDEAL QUANTUM SYSTEMS: GENERAL CONSIDERATIONS 227
6.2.1 EXPANSION IN THE CLASSICAL REGIME 230
6.2.2 FIRST QUANTUM-MECHANICAL CORRECTION TERM 232
6.2.3 RELATIONS BETWEEN THE THERMODYNAMIC POTENTIAL AND OTHER SYSTEM
VARIABLES 233
6.3 THE IDEAL FERMI GAS 234
6.3.1 THE FERMI-DIRAC DISTRIBUTION 234
6.3.2 DETERMINATION O F THE SYSTEM VARIABLES AT LOW TEMPERATURES 237
6.3.3 APPLICATIONS O F THE FERMI-DIRAC DISTRIBUTION 240
6.4 THE IDEAL BOSE GAS 243
6.4.1 PARTICLE NUMBER AND THE BOSE-EINSTEIN DISTRIBUTION 243 6.4.2
BOSE-EINSTEIN CONDENSATION 245
6.4.3 PRESSURE 248
6.4.4 ENERGY AND SPECIFIC HEAT 250
6.4.5 ENTROPY 252
6.4.6 APPLICATIONS O F BOSE STATISTICS 252
6.5 THE PHOTON GAS AND BLACK BODY RADIATION 253
6.5.1 THE KIRCHHOFF LAW 259
6.5.2 THE STEFAN-BOLTZMANN LAW 261
6.5.3 THE PRESSURE O F LIGHT 262
6.5.4 THE TOTAL RADIATIVE POWER OF THE SUN 264
6.5.5 THE COSMIC BACKGROUND RADIATION 266
6.6 LATTICE VIBRATIONS IN SOLIDS: THE PHONON GAS 267
6.7 SYSTEMS WITH INTERNAL DEGREES O F FREEDOM: IDEAL GASES O F MOLECULES
274
6.8 MAGNETIC PROPERTIES OF FERMI SYSTEMS 281
6.8.1 DIAMAGNETISM 281
6.8.2 PARAMAGNETISM 286
6.9 QUASI-PARTICLES 287
6.9.1 MODELS FOR THE MAGNETIC PROPERTIES O F SOLIDS 290
6.9.2 SUPERFLUIDITY 295
7 CHANGES O F EXTERNAL CONDITIONS 297
7.1 REVERSIBLE STATE TRANSFORMATIONS, HEAT, AND WORK 297
7.1.1 FINITE TRANSFORMATIONS OF STATE 300
7.2 CYCLIC PROCESSES 302
7.3 EXERGY AND RELATIVE ENTROPY 306
7.4 TIME DEPENDENCE O F STATISTICAL SYSTEMS 309
PART II ANALYSIS O F STATISTICAL SYSTEMS
8 ESTIMATION O F PARAMETERS 317
8.1 SAMPLES AND ESTIMATORS 318
8.1.1 MONTE CARLO INTEGRATION 321
IMAGE 5
CONTENTS XIII
8.2 CONFIDENCE INTERVALS 325
8.3 PROPAGATION OF ERRORS 328
8.3.1 APPLICATION 330
8.4 THE MAXIMUM LIKELIHOOD ESTIMATOR 331
8.5 THE LEAST-SQUARES ESTIMATOR 336
9 SIGNAL ANALYSIS: ESTIMATION O F SPECTRA 347
9.1 THE SPECTRUM O F A STOCHASTIC PROCESS 347
9.2 THE FOURIER TRANSFORM OF A TIME SERIES AND THE PERIODOGRAM 353 9.3
FILTERS 358
9.3.1 FILTERS AND TRANSFER FUNCTIONS 360
9.3.2 FILTER DESIGN 363
9.4 CONSISTENT ESTIMATION O F SPECTRA 367
9.5 CROSS-SPECTRAL ANALYSIS 375
9.6 FREQUENCY DISTRIBUTIONS FOR NONSTATIONARY TIME SERIES 380
9.7 FILTER BANKS AND DISCRETE WAVELET TRANSFORMATIONS 383
9.7.1 EXAMPLES O F FILTER BANKS 388
9.8 WAVELETS 392
9.8.1 WAVELETS AS BASE FUNCTIONS IN FUNCTION SPACES 392
9.8.2 WAVELETS AND FILTER BANKS 397
9.8.3 SOLUTIONS OF THE DILATION EQUATION 401
10 ESTIMATORS BASED ON A PROBABILITY DISTRIBUTION FOR THE PARAMETERS 405
10.1 BAYESIAN ESTIMATOR AND MAXIMUM A POSTERIORI ESTIMATOR 405 10.2
MARGINALIZATION OF NUISANCE PARAMETERS 407
10.3 NUMERICAL METHODS FOR BAYESIAN ESTIMATORS 412
11 IDENTIFICATION O F STOCHASTIC MODELS FROM OBSERVATIONS 421
11.1 PARAMETER IDENTIFICATION FOR AUTOREGRESSIVE PROCESSES 421
11.2 GRANGER CAUSALITY 427
11.2.1 GRANGER CAUSALITY IN THE TIME DOMAIN 429
11.2.2 GRANGER-CAUSALITY IN THE FREQUENCY DOMAIN 430
11.3 HIDDEN SYSTEMS 432
11.4 THE MAXIMUM A POSTERIORI ESTIMATOR FOR THE INVERSE PROBLEM . . . .
435 11.4.1 THE LEAST SQUARES ESTIMATOR AS A SPECIAL MAP ESTIMATOR 436
11.4.2 . STRATEGIES FOR CHOOSING THE REGULARIZATION PARAMETER. 438
11.4.3 THE REGULARIZATION METHOD 441
11.4.4 EXAMPLES OF THE ESTIMATION OF A DISTRIBUTION FUNCTION BY A
REGULARIZATION METHOD 444
11.5 ESTIMATING THE REALIZATION O F A HIDDEN PROCESS 447
11.5.1 THE VITERBI ALGORITHM 447
11.5.2 THE KALMAN FILTER 450
11.5.3 THE UNSCENTED KALMAN FILTER 460
11.5.4 THE DUAL KALMAN FILTER 463
IMAGE 6
X I V C O N T E N T S
12 ESTIMATING THE PARAMETERS O F A HIDDEN STOCHASTIC MODEL 467
12.1 THE EXPECTATION MAXIMIZATION METHOD (EM METHOD) 468
12.2 ESTIMATING THE PARAMETERS O F A HIDDEN MARKOV MODEL 472
12.2.1 THE FORWARD ALGORITHM 473
12.2.2 THE BACKWARD ALGORITHM 474
12.2.3 THE ESTIMATION FORMULAS 474
12.3 ESTIMATING THE PARAMETERS IN A STATE SPACE MODEL 477
13 STATISTICAL TESTS AND CLASSIFICATION METHODS 4 8 3
13.1 GENERAL COMMENTS CONCERNING STATISTICAL TESTS 483
13.1.1 TEST QUANTITY AND SIGNIFICANCE LEVEL 4 8 3
13.1.2 EMPIRICAL MOMENTS FOR A TEST QUANTITY: THE BOOTSTRAP METHOD 487
13.1.3 THE POWER OF A TEST 489
13.2 SOME USEFUL TESTS 491
13.2.1 THE Z - AND THE T-TEST 491
13.2.2 TEST FOR THE EQUALITY OF THE VARIANCES O F TWO SETS O F
MEASUREMENTS, THE F-TEST 492
13.2.3 THE ^ 2 -TEST 493
13.2.4 THE KOLMOGOROV-SMIRNOV TEST 495
13.2.5 THE F-TEST FOR LEAST-SQUARES ESTIMATORS 496
13.2.6 THE LIKELIHOOD-RATIO TEST 497
13.3 CLASSIFICATION METHODS 499
13.3.1 CLASSIFIERS 500
13.3.2 ESTIMATION OF PARAMETERS THAT ARISE IN CLASSIFIERS 504
13.3.3 AUTOMATIC CLASSIFICATION (CLUSTER ANALYSIS) 505
APPENDIX: RANDOM NUMBER GENERATION FOR SIMULATING REALIZATIONS OF RANDOM
VARIABLES 509
PROBLEMS 511
HINTS AND SOLUTIONS 533
REFERENCES 541
INDEX 547 |
| any_adam_object | 1 |
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| dewey-full | 530.13 |
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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 |
| edition | 3. ed. |
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| indexdate | 2024-08-21T00:08:55Z |
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| isbn | 3642286836 9783642286834 9783642286841 |
| language | English |
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| spelling | Honerkamp, Josef 1941-2022 Verfasser (DE-588)118140361 aut Statistical physics an advanced approach with applications Josef Honerkamp. With collaboration of Björn Schelter 3. ed. Berlin [u.a.] Springer 2012 XIV, 553 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Statistische Physik (DE-588)4057000-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 s DE-604 Schelter, Björn Sonstige (DE-588)132505487 oth text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3976361&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025258425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Honerkamp, Josef 1941-2022 Statistical physics an advanced approach with applications Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 |
| title | Statistical physics an advanced approach with applications |
| title_auth | Statistical physics an advanced approach with applications |
| title_exact_search | Statistical physics an advanced approach with applications |
| title_full | Statistical physics an advanced approach with applications Josef Honerkamp. With collaboration of Björn Schelter |
| title_fullStr | Statistical physics an advanced approach with applications Josef Honerkamp. With collaboration of Björn Schelter |
| title_full_unstemmed | Statistical physics an advanced approach with applications Josef Honerkamp. With collaboration of Björn Schelter |
| title_short | Statistical physics |
| title_sort | statistical physics an advanced approach with applications |
| title_sub | an advanced approach with applications |
| topic | Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistische Physik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3976361&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025258425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT honerkampjosef statisticalphysicsanadvancedapproachwithapplications AT schelterbjorn statisticalphysicsanadvancedapproachwithapplications |