Statistical physics: an advanced approach with applications ; web enhanced with problems and solutions
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Deutsch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Physics and astronomy online library
Advanced texts in physics |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | with 7 tables and 57 problems with solutions |
| Umfang: | XIV, 515 Seiten Illustrationen, Diagramme |
| ISBN: | 9783540430209 9783662047637 3540430202 |
Internformat
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| 100 | 1 | |a Honerkamp, Josef |d 1941-2022 |0 (DE-588)118140361 |4 aut | |
| 245 | 1 | 0 | |a Statistical physics |b an advanced approach with applications ; web enhanced with problems and solutions |c Josef Honerkamp |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XIV, 515 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics and astronomy online library | |
| 490 | 0 | |a Advanced texts in physics | |
| 500 | |a with 7 tables and 57 problems with solutions | ||
| 650 | 4 | |a Statistische Physik | |
| 650 | 4 | |a Statistical physics | |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 08.2003 A 38 0202 PHY 050f 2003 A 58(2) |
|---|---|
| DE-BY-TUM_katkey | 1356041 |
| DE-BY-TUM_location | Mag 02 |
| DE-BY-TUM_media_number | 040005132096 040020728667 |
| _version_ | 1821933159869054976 |
| adam_text | Contents
1
Statistical Physics
Is More than Statistical Mechanics
Part I Modeling of Statistical Systems
2
Random Variables:
Fundamentals of Probability Theory and Statistics
....... 5
2.1
Probability and Random Variables
........................ 6
2.1.1
The Space of Events
.............................. 6
2.1.2
Introduction of Probability
........................ 7
2.1.3
Random Variables
................................ 9
2.2
Multivariate Random Variables
and Conditional Probabilities
............................ 12
2.2.1
Multidimensional Random Variables
................ 12
2.2.2
Marginal Densities
................................ 13
2.2.3
Conditional Probabilities and
Bayes
Theorem
....... 14
2.3
Moments and Quantiles
................................. 18
2.3.1
Moments
........................................ 18
2.3.2
Quantiles
........................................ 22
2.4
The Entropy
........................................... 24
2.4.1
Entropy for a Discrete Set of Events
................ 24
2.4.2
Entropy for a Continuous Space of Events
........... 25
2.4.3
Relative Entropy
................................. 26
2.4.4
Remarks
........................................ 26
2.4.5
Applications
..................................... 27
2.5
Computations with Random Variables
.................... 31
2.5.1
Addition and Multiplication of Random Variables
.... 31
2.5.2
Further Important Random Variables
............... 34
2.5.3
Limit Theorems
.................................. 36
2.6
Stable Random Variables
and Renormalization Transformations
..................... 39
2.6.1
Stable Random Variables
.......................... 39
2.6.2
The Renormalization Transformation
............... 41
2.6.3
Stability Analysis
................................ 42
X
Contents
2.6.4
Scaling Behavior
................................. 44
2.7
The Large Deviation Property for Sums
of Random Variables
.................................... 46
3
Random Variables in State Space:
Classical Statistical Mechanics of Fluids
.................. 51
3.1
The Microcanonical System
.............................. 52
3.2
Systems in Contact
..................................... 55
3.2.1
Thermal Contact
................................. 55
3.2.2
Systems with Exchange of Volume and Energy
....... 63
3.2.3
Systems with Exchange of Particles and Energy
...... 67
3.3
Thermodynamic Potentials
.............................. 70
3.4
Susceptibilities
......................................... 76
3.4.1
Heat Capacities
.................................. 76
3.4.2
Isothermal Compressibility
........................ 78
3.4.3
Isobaric Expansivity
.............................. 79
3.4.4
Isoclioric Tension Coefficient
and Adiabatic Compressibility
..................... 80
3.4.5
A General Relation Between Response Functions
..... 80
3.5
The Equipartition Theorem
.............................. 82
3.6
The Radial Distribution Function
......................... 84
3.7
Approximation Methods
................................. 90
3.7.1
The Virial Expansion
............................. 90
3.7.2
Integral Equations
for the Radial Distribution Function
................ 97
3.7.3
Perturbation Theory
..............................100
3.8
The van
der Waals
Equation
.............................103
3.8.1
The Isotherms
...................................104
3.8.2
The Maxwell Construction
........................105
3.8.3
Corresponding States
.............................108
3.8.4
Critical Exponents
...............................109
3.9
Some General Remarks about Phase Transitions
and Phase Diagrams
....................................112
4
Random Fields:
Textures and Classical Statistical Mechanics
of Spin Systems
..........................................115
4.1
Discrete Stochastic Fields
...............................116
4.1.1
Markov Fields
................................... 117
4.1.2
Gibbs Fields
..................................... 119
4.1.3
Equivalence of Gibbs and Markov Fields
............ 120
4.2
Examples of Markov Random Fields
...................... 121
4.2.1
Model with Independent Random Variables
..........121
4.2.2
Auto Model
.....................................122
4.2.3
Multilevel Logistic Model
..........................123
Contents
XI
4.2.4
Gauss
Model.....................................124
4.3 Characteristic
Quantities of Densities
for Random Fields
......................................124
4.4
Simple Random Fields
..................................127
4.4.1
The White Random Field
or the Ideal Paramagnetic System
..................127
4.4.2
The One-Dimensional Ising Model
..................128
4.5
Random Fields with Phase Transitions
....................132
4.5.1
The Curie Weiss Model
...........................132
4.5.2
The Mean Field Approximation
....................13/3
4.5.3
The Two-Dimensional Ising Model
..................139
4.6
The Landau Free Energy
................................145
4.7
The Renormalization Group Method
for Random Fields and Scaling Laws
......................149
4.7.1
The Renormalization Transformation
...............149
4.7.2
Scaling Laws
.....................................150
Time-Dependent Random Variables:
Classical Stochastic Processes
............................. 155
5.1
Markov Processes
...................................... 156
5.2
The Master Equation
................................... 160
5.3
Examples of Master Equations
........................... 165
5.4
Analytic Solutions of Master Equations
................... 171
5.4.1
Equations for the Moments
........................171
5.4.2
The Equation for the Characteristic Function
........172
5.4.3
Examples
.......................................173
5.5
Simulation of Stochastic Processes and Fields
..............176
5.6
The
Fokker-
Planck Equation
............................184
5.6.1
Fokker-
Planck Equation with Linear Drift Term
and Additive Noise
...............................187
5.7
The Linear Response Function
and the Fluctuation -Dissipation Theorem
.................190
5.8
Approximation Methods
.................................193
5.8.1
The
Ω
Expansion
................................193
5.8.2
The One-Particle Picture
..........................200
5.9
More General Stochastic Processes
........................203
5.9.1
Self-Similar Processes
.............................203
5.9.2
Fractal Brownian Motion
..........................203
5.9.3
Stable Levy Processes
.............................204
5.9.4
Autoregressive
Processes
..........................205
Quantum Random Systems
...............................213
6.1
Quantum-Mechanical Description
of Statistical Systems
...................................213
6.2
Ideal Quantum Systems: General Considerations
...........219
XII Contents
6.2.1 Expansion in
the Classical
Regime..................222
6.2.2 First
Quantum-Mechanical Correction Term
.........223
6.2.3
Relations Between the Thermodynamic Potential
and Other System Variables
.......................224
6.3
The Ideal Fermi Gas
....................................225
6.3.1
The Fermi-Dirac Distribution
......................226
6.3.2
Determination of the System Variables
at Low Temperatures
.............................229
6.3.3
Applications of the Fermi-Dirac Distribution
........231
6.4
The Ideal
Bose
Gas
.....................................234
6.4.1
Particle Number and the Bose-Einstein Distribution
. . 234
6.4.2
Bose-Einstein Condensation
.......................236
6.4.3
Pressure
.........................................239
6.4.4
Energy and Specific Heat
..........................241
6.4.5
Entropy
.........................................243
6.4.6
Applications of
Bose
Statistics
.....................243
6.5
The Photon Gas and Black Body Radiation
................244
6.5.1
The
Kirchhoff
Law
...............................250
6.5.2
The Stefan- Boltzmann Law
.......................252
6.5.3
The Pressure of Light
.............................253
6.5.4
The Total Radiative Power of the Sun
..............255
6.5.5
The Cosmic Background Radiation
.................257
6.6
Lattice Vibrations in Solids: The Phonon Gas
..............257
6.7
Systems with Internal Degrees of Freedom:
Ideal Gases of Molecules
.................................265
6.8
Magnetic Properties of Fermi Systems
.....................271
6.8.1
Diamagnetism
...................................272
6.8.2
Paramagnetism
..................................277
6.9
Quasi-particles
.........................................278
6.9.1
Models for the Magnetic Properties of Solids
.........281
6.9.2
Superfluidity
.....................................286
7
Changes of External Conditions
..........................289
7.1
Reversible State Transformations, Heat, and Work
..........289
7.2
Cyclic Processes
........................................294
7.3
Exergy and Relative Entropy
............................298
7.4
Time Dependence of Statistical Systems
...................301
Part II Analysis of Statistical Systems
8
Estimation of Parameters
.................................309
8.1
Samples and Estimators
.................................310
8.2
Confidence Intervals
....................................317
8.3
Propagation of Errors
...................................320
Contents XIII
8.4
The Maximum Likelihood Estimator
......................322
8.5
The Least-Squares Estimator
............................327
9
Signal Analysis: Estimation of Spectra
.................... 339
9.1
The Discrete Fourier Transform
and the
Periodogram
.................................... 339
9.2
Filters
................................................ 346
9.2.1
Filters and Transfer Functions
..................... 347
9.2.2
Filter Design
.................................... 350
9.3
Consistent Estimation of Spectra
......................... 354
9.4
Frequency Distributions
for Nonstationary Time Series
............................ 363
9.5
Filter Banks and Discrete Wavelet Transformations
......... 366
9.6
Wavelets
.............................................. 376
9.6.1
Wavelets as Base Functions in Function Spaces
....... 377
9.6.2
Wavelets and Filter Banks
......................... 380
9.6.3
Solutions of the Dilation Equation
.................. 382
10
Estimators Based on a Probability Distribution
for the Parameters
.......................................387
10.1
Bayesian Estimator and Maximum a Posteriori Estimator
... 387
10.2
Marginalization of Nuisance Parameters
...................389
10.3
Numerical Methods for Bayesian Estimators
...............394
11
Identification of Stochastic Models from Observations
.... 403
11.1
Hidden Systems
........................................403
11.2
The Maximum a Posteriori (MAP) Estimator
for the Inverse Problem
.................................405
11.2.1
The Least-Squares Estimator
as a Special MAP Estimator
.......................407
11.2.2
Strategies for Choosing the
Regularizat
ion Parameter
. 408
11.2.3
The Regularization Method
........................411
11.2.4
Examples of Estimating a Distribution Function
by a Regularization Method
.......................414
11.3
Estimating the Realization of a Hidden Process
............417
11.3.1
The Viterbi Algorithm
............................417
11.3.2
The
Kalman
Filter
...............................421
12
Estimating the Parameters of a Hidden Stochastic Model
. 431
12.1
The Expectation Maximization Method (EM Method)
......432
12.2
Use of the EM Method for Estimation of the Parameters in
Hidden Systems
........................................434
12.3
Estimating the Parameters of a Hidden Markov Model
......436
12.3.1
The Forward Algorithm
...........................437
12.3.2
The Backward Algorithm
..........................437
XIV Contents
12.3.3
The Estimation Formulas
..........................438
12.4
Estimating the Parameters in a State Space Model
.........441
13
Statistical Tests and Classification Methods
..............445
13.1
General Comments Concerning Statistical Tests
............445
13.1.1
Test Quantity and Significance Level
................445
13.1.2
Empirical Moments for a Test Quantity:
The Bootstrap Method
............................449
13.1.3
The Power of a Test
..............................451
13.2
Some Useful Tests
......................................452
13.2.1
The z- and the i-Test
.............................452
13.2.2
Test for the Equality of the Variances
of Two Sets of Measurements, the F-Test
............454
13.2.3
The x2-Test
.....................................455
13.2.4
The Kolmogorov-Smirnov Test
.....................457
13.2.5
The F-Test for Least-Squares Estimators
............458
13.2.6
The Likelihood-Ratio Test
.........................459
13.3
Classification Methods
..................................461
13.3.1
Classifiers
.......................................462
13.3.2
Estimation of Parameters That Arise in Classifiers
.... 466
13.3.3
Automatic Classification (Cluster Analysis)
..........467
Appendix: Random Number Generation
for Simulating Realizations of Random Variables
.........471
Problems
.....................................................473
Hints and Solutions
...........................................495
References
....................................................503
Index
.........................................................509
|
| any_adam_object | 1 |
| author | Honerkamp, Josef 1941-2022 |
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| dewey-full | 530.1595 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1595 |
| dewey-search | 530.1595 |
| dewey-sort | 3530.1595 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV014171518 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:00:38Z |
| institution | BVB |
| isbn | 9783540430209 9783662047637 3540430202 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009715035 |
| oclc_num | 248242133 |
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| physical | XIV, 515 Seiten Illustrationen, Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Physics and astronomy online library Advanced texts in physics |
| spellingShingle | Honerkamp, Josef 1941-2022 Statistical physics an advanced approach with applications ; web enhanced with problems and solutions Statistische Physik Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 |
| title | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions |
| title_auth | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions |
| title_exact_search | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions |
| title_full | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions Josef Honerkamp |
| title_fullStr | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions Josef Honerkamp |
| title_full_unstemmed | Statistical physics an advanced approach with applications ; web enhanced with problems and solutions Josef Honerkamp |
| title_short | Statistical physics |
| title_sort | statistical physics an advanced approach with applications web enhanced with problems and solutions |
| title_sub | an advanced approach with applications ; web enhanced with problems and solutions |
| topic | Statistische Physik Statistical physics Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistische Physik Statistical physics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009715035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT honerkampjosef statisticalphysicsanadvancedapproachwithapplicationswebenhancedwithproblemsandsolutions |
Inhaltsverzeichnis
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Bibliotheksmagazin
| Signatur: |
0001 08.2003 A 38 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Ausgeliehen – Rückgabe bis: 31.12.9999 |
Teilbibliothek Physik
| Signatur: |
0202 PHY 050f 2003 A 58(2) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |