Statistical physics: an entropic approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2013
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Teilw. angekündigt u.d.T.: Ford, Ian: Statistical thermodynamics |
| Beschreibung: | XIV, 266 S. Ill., graph. Darst. |
| ISBN: | 9781119975304 9781119975311 |
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Datensatz im Suchindex
| _version_ | 1804150182610206721 |
|---|---|
| adam_text | Statistical Physics
An
Entropie
Approach
IAN FORD
Department of Physics and Astronomy, University College London, UK
This undergraduate textbook provides a statistical mechanical foundation to
the classical laws of thermodynamics via a comprehensive treatment of the
basics of classical thermodynamics, equilibrium statistical mechanics, irreversible
thermodynamics, and the statistical mechanics of non-equilibrium phenomena.
This timely book has a unique focus on the concept of entropy, which is studied
starting from the well-known ideal gas law, employing various thermodynamic
processes, example systems and interpretations to expose its role in the second law
of thermodynamics. This modern treatment of statistical physics includes studies of
neutron stars, superconductivity and the recently developed fluctuation theorems.
It also presents figures and problems in a clear and concise way, aiding the
student s understanding.
Statistical Physics: An
Entropie
Approach
•
Provides an excellent introduction to classical thermodynamics
•
Covers key topics within the physics undergraduate curriculum that are
accessible also to students in chemistry and engineering disciplines
•
Dispels confusion
ovar
the nature of entropy, offering a coherent and
consistent treatment of Boltzmann, Gibbs and Shannon models
•
Features clear pictorial representations of statistical systems, illustrating
thermodynamic approaches
•
Develops statistical thermodynamics for a range of systems and applications
•
Features advanced sections on stochastic dynamics and fluctuation relations,
including recent ideas concerning the stochastic definition of entropy
production, together with suggested further reading on these themes.
Also available
as an e-book
■WILEY
ISBN
978-
Ы
19-97 531-1
9 781119»975311
Contents
Preface xiii
1.
Disorder or Uncertainty?
1
2.
Classical Thermodynamics
5
2.1
The Classical Laws of Thermodynamics
5
2.2
Macroscopic State Variables and Thermodynamic Processes
6
2.3
Properties of the Ideal Classical Gas
8
2.4
Thermodynamic Processing of the Ideal Gas
10
2.5
Entropy of the Ideal Gas
13
2.6
Entropy Change in Free Expansion of an Ideal Gas
15
2.7
Entropy Change due to Nonquasistatic Heat Transfer
17
2.8
Cyclic Thermodynamic Processes, the Clausius Inequality
and
Carnoťs
Theorem
19
2.9
Generality of the Clausius Expression for Entropy Change
21
2.10
Entropy Change due to Nonquasistatic Work
23
2.11
Fundamental Relation of Thermodynamics
25
2.12
Entropy Change due to Nonquasistatic Particle Transfer
28
2.13
Entropy Change due to Nonquasistatic Volume Exchange
30
2.14
General Thermodynamic Driving
31
2.15
Reversible and Irreversible Processes
32
2.16
Statements of the Second Law
33
2.17
Classical Thermodynamics: the Salient Points
35
Exercises
35
3.
Applications of Classical Thermodynamics
37
3.1
Fluid Flow and Throttling Processes
37
3.2
Thermodynamic Potentials and Availability
39
3.2.1
Helmholtz Free Energy
40
3.2.2
Why Free Energy?
43
3.2.3
Contrast between Equilibria
43
3.2.4
Gibbs Free Energy
44
3.2.5
Grand Potential
46
3.3
Maxwell Relations
47
3.4 Nonideal
Classical Gas
48
3.5
Relationship between Heat Capacities
49
viii Contents
3.6
General
Expression
for an Adiabat
50
3.7
Determination of Entropy from a Heat Capacity
50
3.8
Determination of Entropy from an Equation of State
51
3.9
Phase Transitions and Phase Diagrams
52
3.9.1
Conditions for Coexistence
53
3.9.2
Clausius-Clapeyron Equation
55
3.9.3
The Maxwell Equal Areas Construction
57
3.9.4
Metastability and Nucleation
59
3.10
Work Processes without Volume Change
59
3.11
Consequences of the Third Law
60
3.12
Limitations of Classical Thermodynamics
61
Exercises
62
4.
Core Ideas of Statistical Thermodynamics
65
4.1
The Nature of Probability
65
4.2
Dynamics of Complex Systems
68
4.2.1
The Principle of Equal a Priori Probabilities
68
4.2.2 Microstate
Enumeration
71
4.3
Microstates and Macrostates
72
4.4
Boltzmann
s
Principle and the Second Law
75
4.5
Statistical Ensembles
77
4.6
Statistical Thermodynamics: the Salient Points
78
Exercises
79
5.
Statistical Thermodynamics of a System of Harmonic Oscillators
81
5.1 Microstate
Enumeration
81
5.2
Microcanonical Ensemble
83
5.3
Canonical Ensemble
84
5.4
The Thermodynamic Limit
88
5.5
Temperature and the Zeroth Law of Thermodynamics
91
5.6
Generalisation
91
Exercises
92
6.
The Boltzmann Factor and the Canonical Partition Function
95
6.1
Simple Applications of the Boltzmann Factor
95
6.1.1
Maxwell-Boltzmann Distribution
95
6.1.2
Single Classical Oscillator and the Equipartition Theorem
97
6.1.3
Isothermal Atmosphere Model
98
6.1.4
Escape Problems and Reaction Rates
99
6.2
Mathematical Properties of the Canonical Partition Function
99
6.3
Two-Level Paramagnet
101
6.4
Single Quantum Oscillator
103
6.5
Heat Capacity of a Diatomic Molecular Gas
104
6.6
Einstein Model of the Heat Capacity of Solids
105
6.7
Vacancies in Crystals
106
Exercises
108
Contents ix
7. The Grand
Canonical
Ensemble and Grand
Partition Function 111
7.1
System of Harmonic Oscillators 111
7.2
Grand Canonical Ensemble for a General System
115
7.3
Vacancies in Crystals Revisited
116
Exercises
127
8.
Statistical Models of Entropy
119
8.1
Boltzmann Entropy
119
8.1.1
The Second Law of Thermodynamics
120
8.1.2
The Maximum Entropy
Macrostate
of Oscillator Spikiness
122
8.1.3
The Maximum Entropy
Macrostate
of Oscillator Populations
122
8.1.4
The Third Law of Thermodynamics
126
8.2
Gibbs Entropy
127
8.2.1
Fundamental Relation of Thermodynamics
and Thermodynamic Work
129
8.2.2
Relationship to Boltzmann Entropy
130
8.2.3
Third Law Revisited
131
8.3
Shannon Entropy
131
8.4
Fine and Coarse Grained Entropy
132
8.5
Entropy at the Nanoscale
133
8.6
Disorder and Uncertainty
134
Exercises
135
9.
Statistical Thermodynamics of the Classical Ideal Gas
137
9.1
Quantum Mechanics of a Particle in a Box
137
9.2
Densities of States
138
9.3
Partition Function of a One-Particle Gas
140
9.4
Distinguishable and Indistinguishable Particles
141
9.5
Partition Function of an N-Particle Gas
145
9.6
Thermal Properties and Consistency with Classical Thermodynamics
146
9.7
Condition for Classical Behaviour
147
Exercises
149
10.
Quantum Gases
151
10.1
Spin and Wavefunction Symmetry
151
10.2 Pauli
Exclusion Principle
152
10.3
Phenomenology of Quantum Gases
153
Exercises
154
11.
Boson Gas 155
11.1
Grand Partition Function for Bosons in a Single Particle State
155
1L2 Bose-Einstein Statistics i56
11.3
Thermal Properties of a Boson Gas
158
11.4
Bose-Einstein Condensation
161
11.5
Cooper Pairs and Superconductivity
166
Exercises
χ
Contents
12. Fermion Gas 169
12.1 Grand Partition
Function
for Fermions
in
a
Single
Particle
State 169
12.2 Fermi-Dirac
Statistics
170
12.3
Thermal Properties of
a
Fermion Gas 171
12.4
Maxwell-Boltzmann Statistics
173
12.5
The Degenerate Fermion Gas
176
12.6
Electron Gas in Metals
177
12.7
White Dwarfs and the Chandrasekhar Limit
179
12.8
Neutron Stars
182
12.9
Entropy of a Black Hole
183
Exercises
184
13.
Photon Gas
187
13.1
Electromagnetic Waves in a Box
187
13.2
Partition Function of the Electromagnetic Field
189
13.3
Thermal Properties of a Photon Gas
191
13.3.1
Planck Energy Spectrum of Black-Body Radiation
191
13.3.2
Photon Energy Density and Flux
193
13.3.3
Photon Pressure
193
13.3.4
Photon Entropy
194
13.4
The Global Radiation Budget and Climate Change
195
13.5
Cosmic Background Radiation
197
Exercises
198
14.
Statistical Thermodynamics of Interacting Particles
201
14.1
Classical Phase Space
201
14.2
Virial Expansion
203
14.3
Harmonic Structures
206
14.3.1
Triatomic Molecule
207
14.3.2
Einstein Solid
208
14.3.3
Debye Solid
209
Exercises
211
15.
Thermodynamics away from Equilibrium
213
15.1
Nonequilibrium Classical Thermodynamics
213
15.1.1
Energy and Particle Currents and their Conjugate
Thermodynamic Driving Forces
213
15.1.2
Entropy Production in Constrained and Evolving Systems
218
15.2
Nonequilibrium Statistical Thermodynamics
220
15.2.1
Probability Flow and the Principle of Equal a
Priori Probabilities
220
15.2.2
The Dynamical Basis of the Principle of Entropy Maximisation
222
Exercises
223
16.
The Dynamics of Probability
225
16.1
The Discrete Random Walk
225
Contents xi
16.2 Master
Equations
226
16.2.1
Solution
to the Random Walk
228
16.2.2
Entropy Production during a Random Walk
229
16.3
The Continuous Random Walk and the Fokker-Planck Equation
230
16.3.1
Wiener Process
232
16.3.2
Entropy Production in the Wiener Process
233
16.4
Brownian Motion
235
16.5
Transition Probability Density for a Harmonic Oscillator
236
Exercises
238
17.
Fluctuation Relations
241
17.1
Forward and Backward Path Probabilities: a Criterion for Equilibrium
241
17.2
Time Asymmetry of Behaviour and a Definition of Entropy Production
243
17.3
The Relaxing Harmonic Oscillator
245
17.4
Entropy Production Arising from a Single Random Walk
247
17.5
Further Fluctuation Relations
249
17.6
The Fundamental Basis of the Second Law
253
Exercises
253
18.
Final Remarks
255
Further Reading
261
Index
263
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:34:52Z |
| institution | BVB |
| isbn | 9781119975304 9781119975311 |
| language | English |
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| spelling | Ford, Ian 1962- Verfasser (DE-588)1035079526 aut Statistical physics an entropic approach Ian Ford Statistical thermodynamics 1. publ. Chichester Wiley 2013 XIV, 266 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teilw. angekündigt u.d.T.: Ford, Ian: Statistical thermodynamics Statistische Physik (DE-588)4057000-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025877373&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025877373&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ford, Ian 1962- Statistical physics an entropic approach Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4123623-3 |
| title | Statistical physics an entropic approach |
| title_alt | Statistical thermodynamics |
| title_auth | Statistical physics an entropic approach |
| title_exact_search | Statistical physics an entropic approach |
| title_full | Statistical physics an entropic approach Ian Ford |
| title_fullStr | Statistical physics an entropic approach Ian Ford |
| title_full_unstemmed | Statistical physics an entropic approach Ian Ford |
| title_short | Statistical physics |
| title_sort | statistical physics an entropic approach |
| title_sub | an entropic approach |
| topic | Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Statistische Physik Lehrbuch |
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