Statistical mechanics: entropy, order parameters, and complexity
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Ausgabe: | Repr. |
| Schriftenreihe: | Oxford master series in physics
14 : Statistical, computational, and theoretical physics |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 349 S. Ill., graph. Darst. |
| ISBN: | 0198566778 019856676X 9780198566762 9780198566779 |
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| 245 | 1 | 0 | |a Statistical mechanics |b entropy, order parameters, and complexity |c James P. Sethna |
| 250 | |a Repr. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XIX, 349 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford master series in physics |v 14 : Statistical, computational, and theoretical physics | |
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Datensatz im Suchindex
| _version_ | 1804143500227248129 |
|---|---|
| adam_text | Contents
List of figures
xv
1
What is statistical mechanics?
1
Exercises
4
1.1
Quantum dice
4
1.2
Probability distributions
5
1.3
Waiting times
6
1.4
Stirling s approximation
7
1.5
Stirling and asymptotic series
7
1.6
Random matrix theory
8
1.7
Six degrees of .separation
9
1.8
Satisfactory map colorings
12
2
Random walks and emergent properties
15
2.1
Random walk examples: universality and scale
invariance
15
2.2
The diffusion equation
19
2.3
Currents and external force«
20
2.4
Solving the diffusion equation
22
2.4.1
Fourier
23
2.4.2
Green
23
Exercises
25
2.1
Random walks in grade
красе
25
2.2
Photon diffusion in the Sun
26
2.3
Molecular motors and random walks
26
2.4
Perfume walk
27
2.5
Generating random walks
28
2.6
Fourier and Green
28
2.7
Periodic diffusion
29
2.S Thermal diffusion
30
2.9
Frying pan
30
2.1Ü
Polymers and random walks
30
2.11
Stock, volatility, and diversification
31
2.12
Computational finance: pricing derivatives
32
2.13
Building a percolation network
33
3
Temperature and equilibrium
37
3.1
The microcanonical ensemble
37
3.2
The imeroeanonical ideal gas
39
3.2.1
Configuration space
39
3.2.2
Momentum space
41
3.3
What is temperature?
44
3.4
Pressure and chemical potential
47
3.4.1
Advanced topic: pressure in mechanics
and statistical mechanics.
48
3.5
Entropy, the ideal gas, and phase-space refinements
51
Exercises
53
3.1
Temperature and energy
54
3.2
Large and very large numbers
54
3.3
Escape velocity
54
3.4
Pressure computation
54
3.5
Hard sphere gas
55
3.6
Connecting two macroscopic systems
55
3.7
Gas mixture
56
3.8
Microcanonical energy fluctuations
56
3.9
Gauss and
Poisson
57
3.10
Triple product relation
58
3.11
Maxwell relations
58
3.12
Solving differential equations: the pendulum
58
Phase-space dynamics and ergodicity
63
4.1
Lionville s theorem
63
4.2
Ergodicity
65
Exercises
69
4.1
Equilibration
69
4.2
Liouville vs. the damped pendulum
70
4.3
Invariant measures
70
4.4
Jupiter! and the
KAM
theorem
72
Entropy
77
5.1
Entropy as irreversibility: engines and the heat death of
the Universe
77
5.2
Entropy as disorder
81
5.2.1
Entropy of mixing: Maxwell s demon and osmotic
pressure
82
5.2.2
Residual entropy of glasses: the roads not taken
83
5.3
Entropy as ignorance: information and memory
85
5.3.1
Non-equilibrium entropy
86
5.3.2
Information entropy
87
Exercises
90
5.1
Life and the heat death of the Universe
91
5.2
Burning information and Maxwellian demons
91
5.3
Reversible computation
93
5.4
Black hole thermodynamics
93
5.5
Pressure-volume diagram
94
5.6
Carnot refrigerator
95
5.7
Does entropy increase?
95
5.8
The
Amoľd
cat map
95
Contents xi
5.9 Chaos,
Lyapunov, and entropy increase
96
5.10
Entropy increases: diffusion
97
5.11
Entropy of glasses
97
5.12
Rubber band
98
5.13
How many shuffles?
99
5.14
Information entropy
100
5.15
Shannon entropy
100
5.16
Fractal dimensions
101
5.17
Deriving entropy
102
Free energies
105
6.1
The canonical ensemble
106
6.2
Uncoupled systems and canonical ensembles
109
6.3
Grand canonical ensemble
112
6.4
What is thermodynamics?
113
6.5
Mechanics: friction and fluctuations
117
6.6
Chemical equilibrium and reaction rates
118
6.7
Free energy density for the ideal gas
121
Exercises
123
6.1
Exponential atmosphere
124
6.2
Two-state system
125
6.3
Negative temperature
125
6.4
Molecular motors and free energies
126
6.5
Laplace
127
6.6 Lagrange 128
6.7
Legendre
128
6.8
Euler
128
6.9
Gibbs-Duhem
129
6.10
Clausius-Clapeyron
129
6.11
Barrier crossing
129
6.12
Michaelis-Menten and Hill
131
6.13
Pollen and hard squares
132
6.14
Statistical mechanics and statistics
133
Quantum statistical mechanics
135
7.1
Mixed states and density matrices
135
7.1.1
Advanced topic: density matrices.
136
7.2
Quantum harmonic oscillator
139
7.3
Bose
and Fermi statistics
140
7.4
Non-interacting bosons and
fermions
141
7.5
Maxwell-Boltzmaim quantum statistics
144
7.6
Black-body radiation and
Bose
condensation
146
7.6.1
Free particles in a box
146
7.6.2
Black-body radiation
147
7.6.3
Boae condensation
148
7.7
Metals and the Fermi gas
150
Exercises
151
7.1
Ensembles and quantum statistics
151
xi:
( unit
ni*
7.2
Phonons and photons are bosons
152
7.3
Phase-space units and the zero of entropy
153
7.4
Does entropy increase in quantum systems?
153
7.5
Photon density matrices
154
7.6
Spin density matrix
154
7.7
Light emission and absorption
154
7.8
Einstein s A and
В
155
7.9
Bosons are gregarious:
superfluide
and lasers
156
7.10
Crystal defects
157
7.11
Phonons on a string
157
7.12
Semiconductors
157
7.13
Bose
condensation in a band
158
7.14
Bose
condensation: the experiment
158
7.15
The photon-dominated Universe
159
7.16
White dwarfs, neutron stars, and black holes
161
Calculation and computation
163
8.1
The Ising model
163
8.1.1
Magnetism
164
8.1.2
Binary alloys
165
8.1.3
Liquids, gases, and the critical point
166
8.1.4
How to solve the Ising model
166
8.2
Markov chains
167
8.3
What is a phase? Perturbation theory
171
Exercises
174
8.1
The Ising model
174
8.2
Ising fluctuations and susceptibilities
174
8.3
Waiting for Godot, and Markov
175
8.4
Red and green bacteria
175
8.5
Detailed balance
176
8.6
Metropolis
176
8.7
Implementing Ising
176
8.8
Wolff
177
8.9
Implementing Wolff
177
8.10
Stochastic cells
178
8.11
The repressilator
179
8.12
Entropy increases! Markov chains
182
8.13
Hysteresis and avalanches
182
8.14
Hysteresis algorithms
185
8.15
NP-completeness and kSAT
186
Order parameters, broken symmetry, and topology
191
9.1
Identify the broken symmetry
192
9.2
Define the order parameter
192
9.3
Examine the elementary excitations
196
9.4
Classify the topological defects
198
Exercises
203
9.1
Topological defects in nematic liquid crystals
203
Contents xiii
9.2 Topological
defects in the XY model
204
9.3
Defect energetics and total divergence terms
205
9.4
Domain walls in magnets
206
9.5
Landau theory for the Ising model
206
9.6
Symmetries and wave equations
209
9.7
Superfluid order and vortices
210
9.8
Superfluids: density matrices and ODLRO
211
10
Correlations, response, and dissipation
215
10.1
Correlation functions: motivation
215
10.2
Experimental probes of correlations
217
10.3
Equal-time correlations in the ideal gas
218
10.4
Onsager s regression hypothesis and time correlations
220
10.5
Susceptibility and linear response
222
10.6
Dissipation and the imaginary part
223
10.7
Static susceptibility
224
10.8
The fluctuation-dissipation theorem
227
10.9
Causality and
Kramers-Krönig 229
Exercises
231
10.1
Microwave background radiation
231
10.2
Pair distributions and molecular dynamics
233
10.3
Damped oscillator
235
10.4
Spin
236
10.5
Telegraph noise in
nano
j
unctions
236
10.6
Fluctuation-dissipation: Ising
237
10.7
Noise and Langevin equations
238
10.8
Magnetic dynamics
238
10.9
Quasiparticle poles and Goldstone s theorem
239
11
Abrupt phase transitions
241
11.1
Stable and
metastabile
phases
241
11.2
Maxwell construction
243
11.3
Nucleation: critical droplet theory
244
11.4
Morphology of abrupt transitions
246
11.4.1
Coarsening
246
11.4.2
Martensites
250
11.4.3
Dendritic growth
250
Exercises
251
11.1
Maxwell and van
der Waals
251
11.2
The van
der Waals
critical point
252
11.3
Interfaces and van
der Waals
252
11.4
Nucleation in the Ising model
253
11.5
Nucleation of dislocation pairs
254
11.6
Coarsening in the Ising model
255
11.7
Origami microstructure
255
11.8
Minimizing sequences and microstructure
258
11.9
Snowflakes and linear stability
259
12
Continuous phase transitions
263
12.1
Universality
265
12.2
Scale
invariance
272
12.3
Examples of critical points
277
12.3.1
Equilibrium criticality: energy versus entropy
278
12.3.2
Quantum criticality: zero-point fluctuations
versus energy
278
12.3.3
Dynamical systems and the onset of chaos
279
12.3.4
Glassy systems: random but frozen
280
12.3.5
Perspectives
281
Exercises
282
12.1
Ising self-similarity
282
12.2
Scaling and corrections to scaling
282
12.3
Scaling and coarsening
282
12.4
Bifurcation theory
283
12.5
Mean-field theory
284
12.6
The onset of lasing
284
12.7
Renormalization-group trajectories
285
12.8
Superconductivity and the renormalization group
286
12.9
Period doubling
288
12.10
The renormalization group and the central limit
theorem: short
291
12.11
The renormalization group and the central limit
theorem: long
291
12.12
Percolation and universality
293
12.13
Hysteresis and avalanches: scaling
296
A Appendix: Fourier methods
299
A.I Fourier conventions
299
A.2 Derivatives, convolutions, and correlations
302
A.3 Fourier methods and function space
303
A.4 Fourier and translational symmetry
305
Exercises 2QY
A.I Sound wave
307
A.2 Fourier cosines
307
A.3 Double sinusoid
307
A.4 Fourier
Gaussiane
308
A.
5
Uncertainty
309
A.
6
Fourier relationships
309
A.7 Aliasing and windowing
310
A.8 White noise
3X1
A.9 Fourier matching 3II
A.
10
Gibbs phenomenon 3II
References
„13
Index
00
q
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| isbn | 0198566778 019856676X 9780198566762 9780198566779 |
| language | English |
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| spelling | Sethna, James P. Verfasser (DE-588)1043838287 aut Statistical mechanics entropy, order parameters, and complexity James P. Sethna Repr. Oxford [u.a.] Oxford Univ. Press 2010 XIX, 349 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford master series in physics 14 : Statistical, computational, and theoretical physics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Mechanik (DE-588)4056999-8 s DE-604 Oxford master series in physics 14 : Statistical, computational, and theoretical physics (DE-604)BV017064373 14 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020722204&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sethna, James P. Statistical mechanics entropy, order parameters, and complexity Oxford master series in physics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4123623-3 |
| title | Statistical mechanics entropy, order parameters, and complexity |
| title_auth | Statistical mechanics entropy, order parameters, and complexity |
| title_exact_search | Statistical mechanics entropy, order parameters, and complexity |
| title_full | Statistical mechanics entropy, order parameters, and complexity James P. Sethna |
| title_fullStr | Statistical mechanics entropy, order parameters, and complexity James P. Sethna |
| title_full_unstemmed | Statistical mechanics entropy, order parameters, and complexity James P. Sethna |
| title_short | Statistical mechanics |
| title_sort | statistical mechanics entropy order parameters and complexity |
| title_sub | entropy, order parameters, and complexity |
| topic | Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistische Mechanik Lehrbuch |
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