Non-equilibrium thermodynamics and physical kinetics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2014
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 359 S. graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783110337693 9783110338355 311033769X |
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Record in the Search Index
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CONTENTS
THE AUTHORS' NOTE V
1 PHENOMENOLOGICAL THERMODYNAMICS OF IRREVERSIBLE PROCESSES 1
1.1 MAIN POSTULATES OF NON-EQUILIBRIUM THERMODYNAMICS 1
1.1.1 THERMODYNAMIC DESCRIPTION OF EQUILIBRIUM AND NON-EQUILIBRIUM
SYSTEMS 1
1.1.2 LOCAL EQUILIBRIUM PRINCIPLE 3
1.1.3 ENTROPY BALANCE EQUATION AND CONSERVATION LAWS 4
1.1.4 GENERALIZED FLOWS AND GENERALIZED THERMODYNAMIC FORCES 7
1.1.5 GENERALIZED TRANSPORT COEFFICIENTS AND THE ONSAGER SYMMETRY
RELATIONS 9
1.1.6 VARIATIONAL PRINCIPLES IN LINEAR NON-EQUILIBRIUM THERMODYNAMICS 10
1.1.7 MINIMUM ENTROPY PRODUCTION PRINCIPLE FOR WEAKLY NON-EQUILIBRIUM
STEADY STATES 12
1.2 ON THE APPLICATION OF THE ONSAGER THEORY 13
1.2.1 THERMOELECTRIC PHENOMENA. THE PELTIER, SEEBECK, THOMSON EFFECTS
AND
THEIR RELATIONSHIP 13
1.2.2 EFFECTS IN AN EXTERNAL MAGNETIC FIELD 19
1.3 SELF-ORGANIZATION IN HIGHLY NON-EQUILIBRIUM SYSTEMS 28
1.3.1 NON-EQUILIBRIUM DISSIPATIVE STRUCTURES 28
1.3.2 THE GLANSDORFF-PRIGOGINE UNIVERSAL EVOLUTION CRITERION 29
1.3.3 WAYS OF DESCRIBING STRONGLY NON-EQUILIBRIUM SYSTEMS 31
1.3.4 STABILITY OF STATES OF HIGHLY NON-EQUILIBRIUM SYSTEMS 34
1.3.5 THE LYAPUNOV GLOBAL STABILITY CRITERION 36
1.3.6 DYNAMICAL SYSTEMS WITH ONE DEGREE OF FREEDOM 38
1.3.7 DYNAMICAL SYSTEMS WITH TWO DEGREES FREEDOM 39
1.3.8 DYNAMIC CHAOS 45
1.3.9 DYNAMIC CHAOS IN ONE-DIMENSIONAL MAPPINGS 51
PROBLEMS TO CHAPTER 1 57
2 BROWNIAN MOTION 59
2.1 THE LANGEVIN EQUATION FOR A BROWNIAN PARTICLE 59
2.1.1 NATURE OF MOTION OF A BROWNIAN PARTICLE. RANDOM FORCES
2.1.2 DISPLACEMENT OF A BROWNIAN PARTICLE 64
2.2 THE FOKKER-PLANCK EQUATION FOR A BROWNIAN PARTICLE
2.2.1 DERIVATION OF THE FOKKER-PLANCK EQUATION 67
2.2.2 THE SOLUTION OF THE FOKKER-PLANCK EQUATION 69
PROBLEMS TO CHAPTER 2 73
HTTP://D-NB.INFO/1042634726
X * CONTENTS
3 KINETIC EQUATIONS IN NON-EQUILIBRIUM STATISTICAL MECHANICS 74
3.1 DESCRIPTION OF NON-EQUILIBRIUM SYSTEMS IN STATISTICAL MECHANICS 74
3.1.1 INTEGRABLE AND NONINTEGRABLE DYNAMICAL SYSTEMS 74
3.1.2 THE EVOLUTION OF DYNAMICAL SYSTEMS IN PHASE SPACE 76
3.2 SUBSTANTIATION OF QUASICLASSICAL KINETIC EQUATIONS 82
3.2.1 THE LIOUVILLE EQUATION FOR THE DISTRIBUTION FUNCTION 82
3.2.2 THE CHAIN OF THE BOGOLIUBOV EQUATIONS 84
3.2.3 EQUATION FOR THE ONE-PARTICLE DISTRIBUTION. THE RELAXATION TIME
APPROXIMATION 88
3.2.4 THE VLASOV KINETIC EQUATION FOR A COLLISIONLESS PLASMA 89
3.2.5 THE BOLTZMANN EQUATION FOR A LOW-DENSITY GAS 96
3.2.6 QUALITATIVE DERIVATION OF THE BOLTZMANN EQUATION 97
3.2.7 DERIVATION OF THE BOLTZMANN EQUATION FROM THE BOGOLIUBOV EQUATIONS
CHAIN 103
3.2.8 THE FOKKER-PLANCK EQUATION 106
3.3 SOLVING FOR KINETIC EQUATIONS 110
3.3.1 THE SOLUTION OF THE BOLTZMANN EQUATION FOR THE EQUILIBRIUM STATE
110
3.3.2 THE BOLTZMANN H-THEOREM 112
3.3.3 THE HILBERT EXPANSION 114
3.3.4 THE ENSKOG-CHAPMAN METHOD. DERIVATION OF HYDRODYNAMIC
EQUATIONS 120
3.3.5 THE METHOD OF MOMENTS 125
PROBLEMS TO CHAPTER 3 127
4 KINETIC EQUATION FOR ELECTRONS AND PHONONS IN CONDUCTING CRYSTALS 129
4.1 KINETIC COEFFICIENTS IN THE RELAXATION TIME APPROXIMATION 129
4.1.1 KINETIC EQUATION FOR ELECTRONS AND ITS SOLUTION TO THE RELAXATION
TIME
APPROXIMATION 129
4.1.2 CONDITIONS OF APPLICABILITY FOR THE QUASI-CLASSICAL DESCRIPTION OF
ELECTRONS IN CONDUCTING CRYSTALS 134
4.1.3 HOW TO DETERMINE CHARGE AND HEAT FLUXES AND CALCULATE KINETIC
COEFFICIENTS WHEN
H =
0 137
4.1.4 SCATTERING OF ELECTRONS BY LATTICE VIBRATIONS 147
4.1.5 THE HAMILTONIAN OF INTERACTION BETWEEN ELECTRONS AND CHARGED
IMPURITY
CENTERS 151
4.1.6 THE COLLISION INTEGRAL FOR THE ELECTRON-PHONON INTERACTION 153
4.1.7 PHENOMENON OF PHONON DRAG 158
4.1.8 EXPRESSIONS FOR CHARGE AND HEAT FLUXES IN A MAGNETIC FIELD. TENSOR
STRUCTURE OF KINETIC COEFFICIENTS 162
4.1.9 GALVANOMAGNETIC AND THERMOMAGNETIC EFFECTS IN SEMICONDUCTORS WITH
A
PARABOLIC DISPERSION LAW 164
CONTENTS
XI
4.2 HYDRODYNAMIC DESCRIPTION OF A HOT ELECTRONS 169
4.2.1 TRANSITION TO A HYDRODYNAMIC DESCRIPTION 169
4.2.2 THE MOMENTUM BALANCE EQUATION 172
4.2.3 BALANCE EQUATIONS OF ENERGY AND PARTICLE NUMBER 178
4.2.4 SOLVING A SET OF BALANCE EQUATIONS. APPLICATIONS OF HYDRODYNAMIC
APPROACH 180
4.2.5 NEGATIVE DIFFERENTIAL RESISTANCE 182
PROBLEMS TO CHAPTER 4 186
5 THEORY OF LINEAR RESPONSE TO AN EXTERNAL MECHANICAL PERTURBATION 189
5.1 ELECTRICAL CONDUCTIVITY OF AN ELECTRON GAS. THE KUBO METHOD 189
5.1.1 THE LIOUVILIE EQUATION AND ITS SOLUTION 189
5.1.2 LINEAR RESPONSE OF A DYNAMICAL SYSTEM TO AN EXTERNAL FIELD 193
5.1.3 CALCULATION OF ELECTRICAL CONDUCTIVITY 197
5.1.4 HIGH-FREQUENCY MAGNETIC SUSCEPTIBILITY 207
5.2 ELECTRICAL CONDUCTIVITY IN A QUANTIZING MAGNETIC FIELD 214
5.2.1 CHARGE AND HEAT FLUXES IN A QUANTIZING MAGNETIC FIELD 214
5.2.2 DYNAMICS OF ELECTRON MOTION IN A QUANTIZING MAGNETIC FIELD 216
5.2.3 THE CONDUCTIVITY TENSOR IN A QUANTIZING MAGNETIC FIELD 218
5.2.4 THE CONDUCTIVITY IN THE CASE QUASIELASTIC SCATTERING BY PHONONS
221
5.3 SYMMETRY PROPERTIES OF CORRELATION FUNCTIONS 227
5.3.1 ADDITIVE CONSERVATION LAWS AND SELECTION RULES FOR AVERAGES 227
5.3.2 SYMMETRY PROPERTIES OF CORRELATION FUNCTIONS FOR OPERATIONS OF
SPATIAL
ROTATION, COMPLEX CONJUGATION AND TIME REVERSAL 230
PROBLEMS TO CHAPTER 5 235
6 NON-EQUILIBRIUM STATISTICAL OPERATOR METHOD 238
6.1 NON-EQUILIBRIUM AND QUASI-EQUILIBRIUM STATISTICAL OPERATORS 238
6.1.1 QUASI-EQUILIBRIUM DISTRIBUTION 238
6.1.2 EXTREMAL PROPERTIES OF A QUASI-EQUILIBRIUM DISTRIBUTION.
THERMODYNAMICS OF A QUASI-EQUILIBRIUM ENSEMBLE 241
6.1.3 BOUNDARY CONDITIONS AND THE LIOUVILLE EQUATION FOR THE NSO 248
6.1.4 LINEAR RELAXATION EQUATIONS IN THE NSO-METHOD 251
6.2 THE PROJECTION OPERATORS METHOD IN NON-EQUILIBRIUM STATISTICAL
MECHANICS 256
6.2.1 WHY IS IT NECESSARY TO INTRODUCE PROJECTION OPERATORS? 256
6.2.2 THE MORI PROJECTION OPERATOR METHOD 260
6.2.3 USING THE MORI PROJECTION OPERATORS TO CALCULATE CONDUCTIVITY 267
6.2.4 RELATIONSHIP BETWEEN A LINEARVARIANTOFTHE NSO-METHOD AND MORI'S
METHOD 274
6.2.5 HIGH-FREQUENCY SUSCEPTIBILITY 277
XII
CONTENTS
6.2.6 DETERMINATION OF NON-EQUILIBRIUM PARAMETERS BY THE NSO-METHOD
279
6.3 HYDRODYNAMIC MODES AND SINGULARITY OF DYNAMIC CORRELATION
FUNCTIONS 285
6.3.1 SPIN DIFFUSION 285
6.3.2 THE FLUCTUATION-DISSIPATION THEOREM 289
6.3.3 LONG-RANGE CORRELATIONS AND SLOW MODES 294
6.3.4 BOGOLIUBOV INEQUALITY AND 1/FC
2
DIVERGENCE THEOREM 298
PROBLEMS TO CHAPTER 6 304
7 RESPONSE OF A HIGHLY NON-EQUILIBRIUM SYSTEM TO A WEAK MEASURING
FIELD 307
7.1 NSO FOR HIGHLY NON-EQUILIBRIUM SYSTEMS 307
7.1.1 SET UP OF THE PROBLEM. A BOUNDARY CONDITION FOR THE NSO 307
7.1.2 GENERALIZED SUSCEPTIBILITY OF A NON-EQUILIBRIUM SYSTEM 313
7.2 PROJECTION OPERATOR FOR NON-EQUILIBRIUM SYSTEMS 317
7.2.1 MAGNETIC SUSCEPTIBILITY 317
7.2.2 ELECTRICAL CONDUCTIVITY OF HIGHLY NON-EQUILIBRIUM SYSTEMS 319
PROBLEMS TO CHAPTER 7 337
8 MASTER EQUATION APPROACH 338
8.1 THE BASIC IDEA OF THE METHOD 338
8.1.1 PROBLEM STATEMENT 338
8.1.2 THE ZWANZIG KINETIC EQUATION 339
8.2 MASTER EQUATION FOR THE QUASI-EQUILIBRIUM DISTRIBUTION 342 -*
8.2.1 ROBERTSON PROJECTION OPERATOR 342
8.2.2 USE OF THE MASTER EQUATION TO CALCULATE KINETIC COEFFICIENTS 345
PROBLEMS TO CHAPTER 8 350
BIBLIOGRAPHY 353
INDEX 355 |
| any_adam_object | 1 |
| author | Bikkin, Halid Ljapilin, Igorʹ I. |
| author_GND | (DE-588)1050273915 |
| author_facet | Bikkin, Halid Ljapilin, Igorʹ I. |
| author_role | aut aut |
| author_sort | Bikkin, Halid |
| author_variant | h b hb i i l ii iil |
| building | Verbundindex |
| bvnumber | BV041584634 |
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| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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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| id | DE-604.BV041584634 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:12:28Z |
| institution | BVB |
| isbn | 9783110337693 9783110338355 311033769X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027029829 |
| oclc_num | 873417604 |
| open_access_boolean | |
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| physical | XII, 359 S. graph. Darst. 240 mm x 170 mm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Bikkin, Halid Verfasser aut Non-equilibrium thermodynamics and physical kinetics Halid Bikkin ; Igor I. Lyapilin Berlin [u.a.] De Gruyter 2014 XII, 359 S. graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd rswk-swf Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 s Kinetische Theorie (DE-588)4030669-0 s DE-604 Ljapilin, Igorʹ I. Verfasser (DE-588)1050273915 aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4467964&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=027029829&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bikkin, Halid Ljapilin, Igorʹ I. Non-equilibrium thermodynamics and physical kinetics Kinetische Theorie (DE-588)4030669-0 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| subject_GND | (DE-588)4030669-0 (DE-588)4130850-5 |
| title | Non-equilibrium thermodynamics and physical kinetics |
| title_auth | Non-equilibrium thermodynamics and physical kinetics |
| title_exact_search | Non-equilibrium thermodynamics and physical kinetics |
| title_full | Non-equilibrium thermodynamics and physical kinetics Halid Bikkin ; Igor I. Lyapilin |
| title_fullStr | Non-equilibrium thermodynamics and physical kinetics Halid Bikkin ; Igor I. Lyapilin |
| title_full_unstemmed | Non-equilibrium thermodynamics and physical kinetics Halid Bikkin ; Igor I. Lyapilin |
| title_short | Non-equilibrium thermodynamics and physical kinetics |
| title_sort | non equilibrium thermodynamics and physical kinetics |
| topic | Kinetische Theorie (DE-588)4030669-0 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| topic_facet | Kinetische Theorie Nichtgleichgewichtsthermodynamik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4467964&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=027029829&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bikkinhalid nonequilibriumthermodynamicsandphysicalkinetics AT ljapilinigorʹi nonequilibriumthermodynamicsandphysicalkinetics |