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E-raamat: Introduction to Statistical Mechanics and Thermodynamics

(Emeritus Professor, Physics Department, Carnegie Mellon University)
  • Formaat: 448 pages
  • Sari: Oxford Graduate Texts
  • Ilmumisaeg: 10-Dec-2019
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780192594631
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  • Formaat: 448 pages
  • Sari: Oxford Graduate Texts
  • Ilmumisaeg: 10-Dec-2019
  • Kirjastus: Oxford University Press
  • Keel: eng
  • ISBN-13: 9780192594631

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An Introduction to Statistical Mechanics and Thermodynamics returns with a second edition which includes new chapters, further explorations, and updated information into the study of statistical mechanics and thermal dynamics.

The first part of the book derives the entropy of the classical ideal gas, using only classical statistical mechanics and an analysis of multiple systems first suggested by Boltzmann. The properties of the entropy are then expressed as "postulates" of thermodynamics in the second part of the book. From these postulates, the formal structure of thermodynamics is developed.

The third part of the book introduces the canonical and grand canonical ensembles, which are shown to facilitate calculations for many model systems. An explanation of irreversible phenomena that is consistent with time-reversal invariance in a closed system is presented.

The fourth part of the book is devoted to quantum statistical mechanics, including black-body radiation, the harmonic solid, Bose-Einstein and Fermi-Dirac statistics, and an introduction to band theory, including metals, insulators, and semiconductors. The final chapter gives a brief introduction to the theory of phase transitions.

Throughout the book, there is a strong emphasis on computational methods to make abstract concepts more concrete.

Arvustused

Review from previous edition In his innovative new text, Carnegie Mellon University physics professor Robert Swendsen presents the foundations of statistical mechanics with, as he puts it, a detour through thermodynamics. That's a desirable strategy because the statistical approach is more fundamental than the classical thermodynamics approach and has many applications to current research problems. [ ] The mathematical notation is carefully introduced and useful; the selected mathematical techniques are clearly explained in a conversational style that both graduate and advanced undergraduate students will find easy to follow. The author's subject organization and conceptual viewpoint address some of the shortcomings of conventional developments of thermal physics and will be helpful to students and researchers seeking a deep appreciation of statistical physics. * Physics Today, August 2013 * Bob Swendsen's book is very well thought out, educationally sound, and more original than other texts. * Jan Tobochnik, Kalamazoo College, USA * Robert Swendsen is a well-respected researcher who has developed many novel algorithms that illustrate his deep understanding of statistical mechanics. His textbook reflects his deep understanding and will likely have a major impact on the way statistical mechanics and thermodynamics is taught. Particularly noteworthy is Swendsen's treatment of entropy, following Boltzmann's original definition in terms of probability, and his comprehensive discussion of the fundamental principles and applications of statistical mechanics and thermodynamics. Students and instructors will enjoy reading the book as much as Swendsen obviously enjoyed writing it. * Harvey Gould, Clark University, USA * In this reader-friendly, excellent text, the author provides a unique combination of the best of two worlds: traditional thermodynamics (following Callen's footsteps) and modern statistical mechanics (including VPython codes for simulations). * Royce Zia, Virginia Polytechnic Institute and State University, USA * Swendsen is famous for developing Monte Carlo algorithms which dramatically speed up the simulation of many systems near a phase transition. The ideas for those algorithms required deep understanding of statistical mechanics, an understanding which is now fully applied to this excellent textbook. * Peter Young, University of California, USA *

1 Introduction
1(10)
1.1 Thermal Physics
1(1)
1.2 What are the Questions?
2(1)
1.3 History
2(2)
1.4 Basic Concepts and Assumptions
4(2)
1.5 Plan of the Book
6(5)
Part I Entropy
2 The Classical Ideal Gas
11(5)
2.1 Ideal Gas
11(1)
2.2 Phase Space of a Classical Gas
12(1)
2.3 Distinguishability
13(1)
2.4 Probability Theory
13(1)
2.5 Boltzmann's Definition of the Entropy
14(1)
2.6 S=klog W
14(1)
2.7 Independence of Positions and Momenta
15(1)
2.8 Road Map for Part I
15(1)
3 Discrete Probability Theory
16(27)
3.1 What is Probability?
16(2)
3.2 Discrete Random Variables and Probabilities
18(1)
3.3 Probability Theory for Multiple Random Variables
19(2)
3.4 Random Numbers and Functions of Random Variables
21(3)
3.5 Mean, Variance, and Standard Deviation
24(1)
3.6 Correlation Function
25(1)
3.7 Sets of Independent Random Numbers
25(2)
3.8 Binomial Distribution
27(2)
3.9 Gaussian Approximation to the Binomial Distribution
29(1)
3.10 A Digression on Gaussian Integrals
30(1)
3.11 Stirling's Approximation for N!
31(3)
3.12 Binomial Distribution with Stirling's Approximation
34(1)
3.13 Multinomial Distribution
35(1)
3.14 Problems
36(7)
4 The Classical Ideal Gas: Configurational Entropy
43(11)
4.1 Separation of Entropy into Two Parts
43(1)
4.2 Probability Distribution of Particles
44(1)
4.3 Distribution of Particles between Two Isolated Systems that were Previously in Equilibrium
45(1)
4.4 Consequences of the Binomial Distribution
46(1)
4.5 Actual Number versus Average Number
47(1)
4.6 The 'Thermodynamic Limit'
48(1)
4.7 Probability and Entropy
48(3)
4.8 The Generalization to M > or = to 2 Systems
51(1)
4.9 An Analytic Approximation for the Configurational Entropy
52(1)
4.10 Problems
53(1)
5 Continuous Random Numbers
54(16)
5.1 Continuous Dice and Probability Densities
54(1)
5.2 Probability Densities
55(2)
5.3 Dirac Delta Functions
57(4)
5.4 Transformations of Continuous Random Variables
61(2)
5.5 Bayes' Theorem
63(2)
5.6 Problems
65(5)
6 The Classical Ideal Gas: Energy Dependence of Entropy
70(11)
6.1 Distribution for the Energy between Two Subsystems
70(2)
6.2 Evaluation of Ωp
72(3)
6.3 Distribution of Energy between Two Isolated Subsystems that were Previously in Equilibrium
75(1)
6.4 Probability Distribution for Large N
76(2)
6.5 The Logarithm of the Probability Distribution and the Energy-Dependent Terms in the Entropy
78(1)
6.6 The Generalization to M > or = to 2 systems
79(2)
7 Classical Gases: Ideal and Otherwise
81(18)
7.1 Entropy of a Composite System of Classical Ideal Gases
81(1)
7.2 Equilibrium Conditions for the Ideal Gas
82(3)
7.3 The Volume-Dependence of the Entropy
85(2)
7.4 Asymmetric Pistons
87(1)
7.5 Indistinguishable Particles
87(2)
7.6 Entropy of a Composite System of Interacting Particles
89(6)
7.7 The Second Law of Thermodynamics
95(1)
7.8 Equilibrium between Subsystems
95(2)
7.9 The Zeroth Law of Thermodynamics
97(1)
7.10 Problems
97(2)
8 Temperature, Pressure, Chemical Potential, and All That
99(16)
8.1 Thermal Equilibrium
99(1)
8.2 What do we Mean by 'Temperature'?
100(1)
8.3 Derivation of the Ideal Gas Law
101(4)
8.4 Temperature Scales
105(1)
8.5 The Pressure and the Entropy
106(1)
8.6 The Temperature and the Entropy
106(1)
8.7 Equilibrium with Asymmetric Pistons, Revisited
107(1)
8.8 The Entropy and the Chemical Potential
108(1)
8.9 The Fundamental Relation and Equations of State
109(1)
8.10 The Differential Form of the Fundamental Relation
109(1)
8.11 Thermometers and Pressure Gauges
110(1)
8.12 Reservoirs
110(1)
8.13 Problems
111(4)
Part II Thermodynamics
9 The Postulates and Laws of Thermodynamics
115(9)
9.1 Thermal Physics
115(2)
9.2 Microscopic and Macroscopic States
117(1)
9.3 Macroscopic Equilibrium States
117(1)
9.4 State Functions
118(1)
9.5 Properties and Descriptions
118(1)
9.6 The Essential Postulates of Thermodynamics
118(2)
9.7 Optional Postulates of Thermodynamics
120(3)
9.8 The Laws of Thermodynamics
123(1)
10 Perturbations of Thermodynamic State Functions
124(8)
10.1 Small Changes in State Functions
124(1)
10.2 Conservation of Energy
125(1)
10.3 Mathematical Digression on Exact and Inexact Differentials
125(3)
10.4 Conservation of Energy Revisited
128(1)
10.5 An Equation to Remember
129(1)
10.6 Problems
130(2)
11 Thermodynamic Processes
132(16)
11.1 Irreversible, Reversible, and Quasi-Static Processes
132(1)
11.2 Heat Engines
133(2)
11.3 Maximum Efficiency
135(1)
11.4 Refrigerators and Air Conditioners
136(1)
11.5 Heat Pumps
137(1)
11.6 The Carnot Cycle
137(2)
11.7 Alternative Formulations of the Second Law
139(1)
11.8 Positive and Negative Temperatures
140(6)
11.9 Problems
146(2)
12 Thermodynamic Potentials
148(11)
12.1 Mathematical Digression: The Legendre Transform
148(4)
12.2 Helmholtz Free Energy
152(1)
12.3 Enthalpy
153(2)
12.4 Gibbs Free Energy
155(1)
12.5 Other Thermodynamic Potentials
155(1)
12.6 Massieu Functions
156(1)
12.7 Summary of Legendre Transforms
156(1)
12.8 Problems
157(2)
13 The Consequences of Extensivity
159(6)
13.1 The Euler Equation
160(1)
13.2 The Gibbs-Duhem Relation
161(1)
13.3 Reconstructing the Fundamental Relation
162(1)
13.4 Thermodynamic Potentials
163(2)
14 Thermodynamic Identities
165(19)
14.1 Small Changes and Partial Derivatives
165(1)
14.2 A Warning about Partial Derivatives
165(1)
14.3 First and Second Derivatives
166(2)
14.4 Standard Set of Second Derivatives
168(1)
14.5 Maxwell Relations
169(1)
14.6 Manipulating Partial Derivatives
170(4)
14.7 Working with Jacobians
174(2)
14.8 Examples of Identity Derivations
176(3)
14.9 General Strategy
179(1)
14.10 Problems
180(4)
15 Extremum Principles
184(11)
15.1 Energy Minimum Principle
185(3)
15.2 Minimum Principle for the Helmholtz Free Energy
188(2)
15.3 Minimum Principle for the Enthalpy
190(1)
15.4 Minimum Principle for the Gibbs Free Energy
191(1)
15.5 Exergy
192(1)
15.6 Maximum Principle for Massieu Functions
193(1)
15.7 Summary
194(1)
15.8 Problems
194(1)
16 Stability Conditions
195(10)
16.1 Intrinsic Stability
195(1)
16.2 Stability Criteria based on the Energy Minimum Principle
196(3)
16.3 Stability Criteria based on the Helmholtz Free Energy Minimum Principle
199(1)
16.4 Stability Criteria based on the Enthalpy Minimization Principle
200(1)
16.5 Inequalities for Compressibilities and Specific Heats
201(1)
16.6 Other Stability Criteria
201(2)
16.7 Problems
203(2)
17 Phase Transitions
205(18)
17.1 The van der Waals Fluid
206(1)
17.2 Derivation of the van der Waals Equation
206(1)
17.3 Behavior of the van der Waals Fluid
207(1)
17.4 Instabilities
208(2)
17.5 The Liquid-Gas Phase Transition
210(2)
17.6 Maxwell Construction
212(1)
17.7 Coexistent Phases
212(1)
17.8 Phase Diagram
213(1)
17.9 Helmholtz Free Energy
214(2)
17.10 Latent Heat
216(1)
17.11 The Clausius-Clapeyron Equation
217(1)
17.12 Gibbs' Phase Rule
218(1)
17.13 Problems
219(4)
18 The Nernst Postulate: The Third Law of Thermodynamics
223(8)
18.1 Classical Ideal Gas Violates the Nernst Postulate
223(1)
18.2 Planck's Form of the Nernst Postulate
224(1)
18.3 Consequences of the Nernst Postulate
224(1)
18.4 Coefficient of Thermal Expansion at Low Temperatures
225(1)
18.5 The Impossibility of Attaining a Temperature of Absolute Zero
226(1)
18.6 Summary and Signposts
226(1)
18.7 Problems
227(4)
Part III Classical Statistical Mechanics
19 Ensembles in Classical Statistical Mechanics
231(27)
19.1 Microcanonical Ensemble
232(1)
19.2 Molecular Dynamics: Computer Simulations
232(2)
19.3 Canonical Ensemble
234(3)
19.4 The Partition Function as an Integral over Phase Space
237(1)
19.5 The Liouville Theorem
238(2)
19.6 Consequences of the Canonical Distribution
240(1)
19.7 The Helmholtz Free Energy
241(1)
19.8 Thermodynamic Identities
242(1)
19.9 Beyond Thermodynamic Identities
243(1)
19.10 Integration over the Momenta
244(1)
19.11 Monte Carlo Computer Simulations
245(4)
19.12 Factorization of the Partition Function: The Best Trick in Statistical Mechanics
249(1)
19.13 Simple Harmonic Oscillator
250(2)
19.14 Problems
252(6)
20 Classical Ensembles: Grand and Otherwise
258(8)
20.1 Grand Canonical Ensemble
258(1)
20.2 Grand Canonical Probability Distribution
259(2)
20.3 Importance of the Grand Canonical Partition Function
261(1)
20.4 Z(T,V,µ) for the Ideal Gas
262(1)
20.5 Summary of the Most Important Ensembles
263(1)
20.6 Other Classical Ensembles
264(1)
20.7 Problems
264(2)
21 Refining the Definition of Entropy
266(5)
21.1 The Canonical Entropy
266(2)
21.2 The Grand Canonical Entropy
268(2)
21.3 Problems
270(1)
22 Irreversibility
271(14)
22.1 What Needs to be Explained?
271(1)
22.2 Trivial Form of Irreversibility
272(1)
22.3 Boltzmann's H-Theorem
272(1)
22.4 Loschmidt's Umkehreinwand
272(1)
22.5 Zermelo's Wiederkehreinwand
273(1)
22.6 Free Expansion of a Classical Ideal Gas
273(5)
22.7 Zermelo's Wiederkehreinwand Revisited
278(1)
22.8 Loschmidt's Umkehreinwand Revisited
278(1)
22.9 What is 'Equilibrium'?
279(1)
22.10 Entropy
279(2)
22.11 Interacting Particles
281(4)
Part IV Quantum Statistical Mechanics
23 Quantum Ensembles
285(12)
23.1 Basic Quantum Mechanics
286(1)
23.2 Energy Eigenstates
287(3)
23.3 Many-Body Systems
290(1)
23.4 Two Types of Probability
290(3)
23.5 The Density Matrix
293(1)
23.6 Uniqueness of the Ensemble
294(1)
23.7 The Planck Entropy
295(1)
23.8 The Quantum Microcanonical Ensemble
296(1)
24 Quantum Canonical Ensemble
297(25)
24.1 Derivation of the QM Canonical Ensemble
297(2)
24.2 Thermal Averages and the Average Energy
299(1)
24.3 The Quantum Mechanical Partition Function
299(3)
24.4 The Quantum Mechanical Entropy
302(1)
24.5 The Origin of the Third Law of Thermodynamics
303(2)
24.6 Derivatives of Thermal Averages
305(1)
24.7 Factorization of the Partition Function
306(2)
24.8 Special Systems
308(1)
24.9 Two-Level Systems
309(2)
24.10 Simple Harmonic Oscillator
311(2)
24.11 Einstein Model of a Crystal
313(2)
24.12 Problems
315(7)
25 Black-Body Radiation
322(9)
25.1 Black Bodies
322(1)
25.2 Universal Frequency Spectrum
322(1)
25.3 A Simple Model
323(1)
25.4 Two Types of Quantization
323(2)
25.5 Black-Body Energy Spectrum
325(3)
25.6 Total Energy
328(1)
25.7 Total Black-Body Radiation
329(1)
25.8 Significance of Black-Body Radiation
329(1)
25.9 Problems
330(1)
26 The Harmonic Solid
331(19)
26.1 Model of a Harmonic Solid
331(1)
26.2 Normal Modes
332(4)
26.3 Transformation of the Energy
336(2)
26.4 The Frequency Spectrum
338(2)
26.5 Alternate Derivation: Equations of Motion
340(1)
26.6 The Energy in the Classical Model
341(1)
26.7 The Quantum Harmonic Crystal
342(1)
26.8 Debye Approximation
343(5)
26.9 Problems
348(2)
27 Ideal Quantum Gases
350(19)
27.1 Single-Particle Quantum States
350(2)
27.2 Density of Single-Particle States
352(1)
27.3 Many-Particle Quantum States
353(2)
27.4 Quantum Canonical Ensemble
355(1)
27.5 Grand Canonical Ensemble
355(1)
27.6 A New Notation for Energy Levels
356(1)
27.7 Exchanging Sums and Products
357(1)
27.8 Grand Canonical Partition Function for Independent Particles
358(1)
27.9 Distinguishable Quantum Particles
359(1)
27.10 Sneaky Derivation of PV =NkBT
360(1)
27.11 Equations for U = (E) and (N)
360(2)
27.12 (na) for Bosons
362(1)
27.13 (na) for Fermions
362(1)
27.14 Summary of Equations for Fermions and Bosons
363(1)
27.15 Integral Form of Equations for N and U
364(1)
27.16 Basic Strategy for Fermions and Bosons
365(1)
27.17 P = 2U/3V
365(2)
27.18 Problems
367(2)
28 Bose-Einstein Statistics
369(17)
28.1 Basic Equations for Bosons
369(1)
28.2 (na) for Bosons
369(1)
28.3 The Ideal Bose Gas
370(1)
28.4 Low-Temperature Behavior of µ
371(2)
28.5 Bose-Einstein Condensation
373(1)
28.6 Below the Einstein Temperature
373(2)
28.7 Energy of an Ideal Gas of Bosons
375(1)
28.8 What About the Second-Lowest Energy State?
376(1)
28.9 The Pressure below T < TE
377(1)
28.10 Transition Line in P-V Plot
378(1)
28.11 A Numerical Approach to Bose-Einstein Statistics
378(2)
28.12 Problems
380(6)
29 Fermi-Dirac Statistics
386(18)
29.1 Basic Equations for Fermions
386(1)
29.2 The Fermi Function and the Fermi Energy
387(1)
29.3 A Useful Identity
388(1)
29.4 Systems with a Discrete Energy Spectrum
389(1)
29.5 Systems with Continuous Energy Spectra
390(1)
29.6 Ideal Fermi Gas
391(1)
29.7 Fermi Energy
391(1)
29.8 Compressibility of Metals
392(1)
29.9 Sommerfeld Expansion
393(3)
29.10 General Fermi Gas at Low Temperatures
396(2)
29.11 Ideal Fermi Gas at Low Temperatures
398(1)
29.12 Problems
399(5)
30 Insulators and Semiconductors
404(19)
30.1 Tight-Binding Approximation
404(2)
30.2 Bloch's Theorem
406(2)
30.3 Nearly-Free Electrons
408(2)
30.4 Energy Bands and Energy Gaps
410(1)
30.5 Where is the Fermi Energy?
411(1)
30.6 Fermi Energy in a Band (Metals)
412(1)
30.7 Fermi Energy in a Gap
412(4)
30.8 Intrinsic Semiconductors
416(1)
30.9 Extrinsic Semiconductors
416(2)
30.10 Semiconductor Statistics
418(4)
30.11 Semiconductor Physics
422(1)
31 Phase Transitions and the Ising Model
423(24)
31.1 The Ising Chain
424(1)
31.2 The Ising Chain in a Magnetic Field (J = 0)
425(1)
31.3 The Ising Chain with h = 0, but F not = to 0
426(2)
31.4 The Ising Chain with both F not = to 0 and h not = to 0
428(4)
31.5 Mean-Field Approximation
432(4)
31.6 Critical Exponents
436(1)
31.7 Mean-Field Exponents
437(1)
31.8 Analogy with the van der Waals Approximation
438(1)
31.9 Landau Theory
439(1)
31.10 Beyond Landau Theory
440(1)
31.11 Problems
441(6)
Appendix: Computer Calculations and Python 447(10)
A.1 MatPlotLib
447(2)
A.2 Python
449(1)
A.3 Histograms
449(1)
A.4 The First Python Program
450(1)
A.5 Python Functions
451(1)
A.6 Graphs
452(1)
A.7 Reporting Python Results
453(2)
A.8 Timing Your Program
455(1)
A.9 Molecular Dynamics
455(1)
A.10 Courage
456(1)
Index 457
Robert Swendsen received his BS from Yale and his PhD from the University of Pennsylvania. He did postdoctoral work at the Universität zu Köln, Germany, the Kernforschungsanlage in Jülich, Germany, and Brookhaven National Laboratory. From 1978 to 1984 he worked at the IBM Zurich Research Center. In 1984, he joined Carnegie Mellon University.

He is a Fellow of both the American Physical Society and the American Association for the Advancement of Science. He was given an IBM Outstanding Achievement Award in 1981 and shared a Forefronts of Large-Scale Computational Problems Award with S. Kumar, J.M. Rosenberg, and P.A. Kollman in 1991. He was awarded the 2014 Aneesur Rahman Prize for Computational Physics and the 2014 Julius Ashkin Teaching Award in the Mellon College of Science at Carnegie Mellon University.