Nonequilibrium statistical physics: linear irreversible processes
Literaturverz. S.
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2010
|
| Series: | Oxford graduate texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Literaturverz. S. |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xix, 491 Seiten Diagramme |
| ISBN: | 9780199556885 9780198712275 |
Staff View
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| 245 | 1 | 0 | |a Nonequilibrium statistical physics |b linear irreversible processes |c Noëlle Pottier |
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| 300 | |a xix, 491 Seiten |b Diagramme | ||
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Record in the Search Index
| _version_ | 1804139406754316288 |
|---|---|
| adam_text | Contents
Chapter
1
Random variables and random processes
1
1
Random variables, moments, and characteristic function
2
2
Multivariate distributions
4
3
Addition of random variables
6
4
Gaussian distributions
7
5
The central limit theorem
9
6
Random processes
12
7
Stationarity and ergodicity
14
8
Random processes in physics: the example of Brownian motion
16
9
Harmonic analysis of stationary random processes
17
10
The Wiener Khintchine theorem
19
Appendix
1A An alternative derivation of the Wiener-Khintchine theorem
23
Bibliography
25
References
25
Chapter
2
Linear thermodynamics of irreversible processes
27
1
A few reminders of equilibrium thermodynamics
28
2
Description of irreversible processes: affinities and fluxes
29
3
The local equilibrium hypothesis
32
4
Affinities and fluxes in a continuous medium in local equilibrium
34
5
Linear response
37
6
A few simple examples of transport coefficients
38
7
Curie s principle
42
8
The reciprocity relations
43
9
Justification of the reciprocity relations
45
10
The minimum entropy production theorem
48
Bibliography
50
References
50
xii Contents
Supplement 2A
Thermodynamic
fluctuations
51
1 The
fluctuations
51
2
Consequences of the maximum entropy principle
52
3
Probability of a fluctuation: the Einstein formula
53
4
Equilibrium fluctuations in a fluid of ./V molecules
54
Bibliography
58
References
58
Supplement 2B
Thermoelectric effects
59
1
Introduction
59
2
The entropy source
60
3
Isothermal electrical conduction
61
4
Open-circuit thermal conduction
62
5
The Seebeck effect
62
6
The Peltier effect
63
7
The Thomson effect
65
8
An illustration of the minimum entropy production theorem
66
Bibliography
67
Supplement 2C
Thermodiffusion in a fluid mixture
68
1
Introduction
68
2
Diffusive fluxes in a binary mixture
68
3
The entropy source
69
4
Linear relations between fluxes and affinities
70
5
The Soret and Dufour effects
72
Bibliography
73
References
73
Chapter
3
Statistical description of out-of-equilibrium systems
75
1
The phase space distribution function
76
2
The density operator
80
3
Systems at equilibrium
83
4
Evolution of the macroscopic variables: classical case
84
5
Evolution of the macroscopic variables: quantum case
86
Bibliography
88
Chapter
4
Classical systems: reduced distribution functions
89
1
Systems of classical particles with pair interactions
90
2
The Liouville equation
91
3
Reduced distribution functions: the BBGKY hierarchy
93
4
The
Vlasov
equation
96
5
Gauge
invariance
97
Contents xiii
Appendices
4A
Pair interaction potentials
99
4B Hamilton s equations for a charged particle
100
4C Gauge
invariance
of the Liouville equation
102
Bibliography
104
Chapter
5
The Boltzmann equation
105
1
Statistical description of dilute classical gases
106
2
Time and length scales
107
3
Notations and definitions
108
4
Evolution of the distribution function
109
5
Binary collisions
110
6
The Boltzmann equation
113
7
Irreversibility
116
8
The
Я
-theorem
117
9
Equilibrium distributions
120
10
Global equilibrium
121
11
Local equilibrium
123
Bibliography
125
References
125
Supplement 5A
The
Lorentz gas
126
1
Gas in the presence of fixed scattering centers
126
2
Time scales
126
3
Collisions with the fixed scatterers
127
4
Kinetic equation of the
Lorentz gas
127
Bibliography
130
References
130
Supplement 5B
The irreversibility paradoxes
131
1
The paradoxes
131
2
The time-reversal paradox
131
3
The recurrence paradox
132
Bibliography
133
References
133
Chapter
6
Transport coefficients
135
1
The relaxation time approximation
136
2
Linearization with respect to the external perturbations
138
3
Kinetic coefficients of
a Lorentz gas
138
4
Electrical conductivity
142
5
Diffusion coefficient
144
Bibliography
147
References
147
xiv Contents
Supplement 6A
Landau
damping
148
1
Weakly coupled plasma
148
2
The
Vlasov
equations for a collisionless plasma
148
3
Conductivity and electrical permittivity of a collisionless plasma
151
4
Longitudinal waves in a Maxwellian plasma
154
Bibliography
157
Chapter
7
Prom the Boltzmann equation to the hydrodynamic equations
159
1
The hydrodynamic regime
160
2
Local balance equations
161
3
The Chapman-Enskog expansion
165
4
The zeroth-order approximation
168
5
The first-order approximation
169
Appendices
7
A A property of the collision integral
175
7B Newton s law and viscosity coefficient
176
Bibliography
180
Chapter
8
The Bloch—Boltzmann theory of electronic transport
181
1
The Boltzmann equation for the electron gas
182
2
The Boltzmann equation s collision integral
184
3
Detailed balance
187
4
The linearized Boltzmann equation
188
5
Electrical conductivity
189
6
Semiclassical transport in the presence of a magnetic field
192
7
Validity limits of the Bloch-Boltzmann theory
198
Bibliography
200
References
200
Supplement 8A
Collision processes
201
1
Introduction
201
2
Electron-impurity scattering
201
3
Electron-phonon scattering
207
Bibliography
211
References
211
Supplement 8B
Thermoelectric coefficients
212
1
Particle and heat fluxes
212
2
General expression for the kinetic coefficients
213
3
Thermal conductivity
213
4
The Seebeck and Peltier coefficients
215
Bibliography
217
Contents xv
Chapter
9
Master
equations
219
1
Markov processes: the Chapman-Kolmogorov equation
220
2
Master equation for a Markovian random process
223
3
The
Pauli
master equation
226
4
The generalized master equation
228
5
Prom the generalized master equation to the
Pauli
master equation
229
6
Discussion
231
Bibliography
233
References
233
Chapter
10
Brownian motion: the
Langevin
model
235
1
The
Langevin
model
236
2
Response and relaxation
238
3
Equilibrium velocity fluctuations
243
4
Harmonic analysis of the
Langevin
model
247
5
Time scales
249
Bibliography
251
References
251
Supplement 10A
The generalized
Langevin
model
253
1
The generalized
Langevin
equation
253
2
Complex admittance
255
3
Harmonic analysis of the generalized
Langevin
model
255
4
An analytical model
257
Bibliography
259
References
259
Supplement 10B
Brownian motion in a bath of oscillators
260
1
The Caldeira-Leggett model
260
2
Dynamics of the Ohmic free particle
265
3
The quantum
Langevin
equation
267
Bibliography
269
References
269
Supplement IOC
The Nyquist theorem
270
1
Thermal noise in an electrical circuit
270
2
The Nyquist theorem
270
Bibliography
275
References
275
xvi Contents
Chapter
11
Brownian
motion: the Fokker-Planck equation
277
1
Evolution of the velocity distribution function
278
2
The Kramers-Moyal expansion
279
3
The Fokker-Planck equation
282
4
Brownian motion and Markov processes
285
Bibliography
288
References
288
Supplement
11
A
Random walk
290
1
The drunken walker
290
2
Diffusion of a drunken walker on a lattice
291
3
The diffusion equation
292
Bibliography
293
References
293
Supplement 11B
Brownian motion: Gaussian processes
294
1
Harmonic analysis of stationary Gaussian processes
294
2
Gaussian Markov stationary processes
295
3
Application to Brownian motion
297
Bibliography
300
References
300
Chapter
12
Linear responses and equilibrium correlations
301
1
Linear response functions
302
2
Generalized susceptibilities
303
3
The Kramers-Kronig relations
306
4
Dissipation
307
5
Non-uniform phenomena
308
6
Equilibrium correlation functions
310
7
Properties of the equilibrium autocorrelation functions
314
Appendix
12A An alternative derivation of the Kramers-Kronig relations
319
Bibliography
321
References
321
Supplement 12A
Linear response of a damped oscillator
322
1
General interest of the study
322
2
The undamped oscillator
322
3
Oscillator damped by viscous friction
323
4
Generalized susceptibility
324
5
The displacement response function
327
Bibliography
328
Contents xvü
Supplement 12B
Electronic
polarization
329
1
Semiclassical model
329
2
Polarization response function
330
3
Generalized susceptibility
331
4
Comparison with the
Lorentz
model
331
Bibliography
334
Supplement 12C
Some examples of dynamical structure factors
335
1
The examples
335
2
Free atom
335
3
Atom in a harmonic potential
337
Bibliography
340
Chapter
13
General linear response theory
341
1
The object of linear response theory
342
2
First-order evolution of the density operator
342
3
The linear response function
345
4
Relation with the canonical correlation function
347
5
Generalized susceptibility
348
6
Spectral function
350
7
Relaxation
352
8
Symmetries of the response and correlation functions
357
9
Non-uniform phenomena
359
Appendices
13A Classical linear response
361
13B Static susceptibility of an isolated system and isothermal susceptibility
363
Bibliography
367
References
367
Supplement 13A
Dielectric relaxation
368
1
Dielectric permittivity and polarizability
368
2
Microscopic polarization mechanisms
371
3
The Debye theory of dielectric relaxation
371
4
A microscopic model of orientational polarization
374
Bibliography
378
References
378
Supplement 13B
Magnetic resonance
379
1
Formulation of the problem
379
2
Phenomenological theory
380
3
A microscopic model
383
Bibliography
388
xviii Contents
Chapter
14
The fluctuation-dissipation theorem
389
1
Dissipation
390
2
Equilibrium fluctuations
393
3
The fluctuation-dissipation theorem
395
4
Positivity
of
ωχ ΑΑ (ω)
398
5
Static susceptibility
398
6
Sum rules
400
Bibliography
403
References
403
Supplement 14A
Dissipative dynamics of a harmonic oscillator
404
1
Oscillator coupled with a thermal bath
404
2
Dynamics of the uncoupled oscillator
404
3
Response functions and susceptibilities of the coupled oscillator
407
4
Analysis of
χχχ{ω)
409
5
Dynamics of the weakly coupled oscillator
415
Bibliography
417
References
417
Chapter
15
Quantum theory of electronic transport
419
1
The Kubo-Nakano formula
420
2
The Kubo-Greenwood formula
423
3
Conductivity of an electron gas in the presence of impurities
427
Bibliography
431
References
431
Supplement 15A
Conductivity of a weakly disordered metal
433
1
Introduction
433
2
The Kubo-Greenwood formula
433
3
Conductivity of a macroscopic system
436
4
Conductance of a mesoscopic system: Landauer s approach
438
5
Addition of quantum resistances in series: localization
440
Bibliography
445
References
445
Chapter
16
Thermal transport coefficients
447
1
The indirect
Kubo
method
448
2
The source of entropy and the equivalent Hamiltonian
452
Bibliography
457
References
457
Contents xix
Supplement 16A
Diffusive light waves
458
1
Diffusive light transport
458
2
Diffusion coefficient of light intensity
459
3
Diffusive wave spectroscopy
462
Bibliography
467
References
467
Supplement 16B
Light scattering by a fluid
468
1
Introduction
468
2
Linearized hydrodynamic equations
468
3
Transverse fluctuations
470
4
Longitudinal fluctuations
472
5
Dynamical structure factor
478
Bibliography
480
References
480
Index
481
|
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| series2 | Oxford graduate texts |
| spelling | Pottier, Noëlle Verfasser aut Nonequilibrium statistical physics linear irreversible processes Noëlle Pottier Oxford Oxford University Press 2010 xix, 491 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Hier auch später erschienene, unveränderte Nachdrucke Literaturverz. S. Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Irreversibler Prozess (DE-588)4027687-9 gnd rswk-swf Nichtgleichgewichtsstatistik (DE-588)4136220-2 s DE-604 Statistische Physik (DE-588)4057000-9 s Irreversibler Prozess (DE-588)4027687-9 s Erscheint auch als Online-Ausgabe 978-0-19-157427-6 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pottier, Noëlle Nonequilibrium statistical physics linear irreversible processes Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Statistische Physik (DE-588)4057000-9 gnd Irreversibler Prozess (DE-588)4027687-9 gnd |
| subject_GND | (DE-588)4136220-2 (DE-588)4057000-9 (DE-588)4027687-9 |
| title | Nonequilibrium statistical physics linear irreversible processes |
| title_auth | Nonequilibrium statistical physics linear irreversible processes |
| title_exact_search | Nonequilibrium statistical physics linear irreversible processes |
| title_full | Nonequilibrium statistical physics linear irreversible processes Noëlle Pottier |
| title_fullStr | Nonequilibrium statistical physics linear irreversible processes Noëlle Pottier |
| title_full_unstemmed | Nonequilibrium statistical physics linear irreversible processes Noëlle Pottier |
| title_short | Nonequilibrium statistical physics |
| title_sort | nonequilibrium statistical physics linear irreversible processes |
| title_sub | linear irreversible processes |
| topic | Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd Statistische Physik (DE-588)4057000-9 gnd Irreversibler Prozess (DE-588)4027687-9 gnd |
| topic_facet | Nonequilibrium statistical mechanics Nichtgleichgewichtsstatistik Statistische Physik Irreversibler Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pottiernoelle nonequilibriumstatisticalphysicslinearirreversibleprocesses |