Fundamental theories, such as classical mechanics, electrodynamics, and quantum mechanics, aim to understand the world in terms of basic constituents and fundamental interactions. Thermodynamics, an older science concerned with the thermal characteristics of liquids and gases, gave rise to statistical mechanics. It grew up around it before absorbing it. Statistical mechanics has come a long way from these humble beginnings, but thermodynamics remains a vital field in and of itself. The main purpose of statistical thermodynamics (also known as equilibrium statistical mechanics) is to infer the classical thermodynamics of materials from their constituent particles' characteristics and interactions. To put it another way, statistical thermodynamics connects the macroscopic properties of materials in thermodynamic equilibrium with the microscopic behaviours and motions that occur within the material. While statistical mechanics is concerned with dynamics in general, the focus here is on statistical equilibrium. Statistical equilibrium does not imply that the particles have ceased to move, but rather that the ensemble has reached a state of inertia.
The book examines, analyses, and upholds the pillars of thermodynamics & statistical mechanics and their importance in today's world. It goes over the principles and methods that have been created in this subject in great depth. This book is a comprehensive collection of chapters that cover everything from the fundamentals to the most advanced ideas. It deals with statistical physics, thermodynamic functions, canonical distribution, ideal gases and quantum statistics of ideal gases. It also focuses on electron gas in a magnetic field, magnetic and dielectric materials, lattice dynamics, condensed bodies, functional integration in statistical physics and macroscopic quantum effects. It can be used as a complement to existing books and for supplementary reading. The book is excellent for people who want to learn more about this topic in depth.
Preface ix
1. Basic Principles of Statistical Physics 1
1. Introduction 1
2. Microscopic and Macroscopic Description of States 2
3. Basic Postulates 3
4. Gibbs Ergodic Assumption 4
5. Gibbsian Ensembles 8
6. Experimental Basis of Statistical Mechanics 12
7. Definition of Expectation values 13
8. Ergodic Principle and Expectation Values 13
9. Properties of Distribution Functions 14
10. About Probabilities 14
11. Relative Fluctuation of an Additive Macroscopic Parameter 17
12. Liouville Theorem 18
13. Gibbs Microcanonical Ensemble 19
14. Microcanonical Distribution in Quantum Mechanics 20
Epilogue 21
References 21
2. Thermodynamic Functions 24
1. Introduction 24
2. Temperature 24
3. Adiabatic Processes 25
4. Thermodynamic Identity 27
5. Laws of Thermodynamics 28
6. First Law of Thermodynamics 29
7. Second Law of Thermodynamics 30
8. Heat Capacity and Equation of State 36
9. Jacobian Method 37
10. Joule-Thomson Process 38
11. Condition for Equilibrium and Stability in an Isolated System 39
Epilogue 46
References 46
3. Canonical Distribution 48
1. Introduction 48
2. Gibbs Canonical Distribution 48
3. Maxwell Distribution 52
4. Experimental Basis of Statistical Mechanics 54
5. Grand Canonical Distribution 55
6. Thermodynamics in the microcanonical ensemble 58
7. Simulation in the MIcrocanonical Ensemble: Molecular Dynamics 59
Epilogue 59
References 60
4. Ideal Gases 62
1. Introduction 62
2. Boltzmann Distribution 63
3. Entropy of a Nonequilibrium Boltzmann Gas 65
4. Monatomic Gas 70
5. Electronic Angular Momentum Effect 70
6. Specific Heats 73
Epilogue 74
References 74
5. Quantum Statistics of Ideal Gases 77
1. Introduction 77
2. Maxwell-Boltzmann, Bose-Einstein and Fermi- Dirac Statistics 77
3. Entropy of Non-equilibrium Fermi and Bose Gases 78
4. Fermi Gas 85
5. Bose Gas 86
6. Thermodynamic Functions for Quantum Gases 88
7. Fermi Energy 90
8. Degenerate Electronic Gas at Temperature Different from Zero 92
9. Application of Statistics to an Intrinsic Semiconductor 95
10. Equilibrium or Black Body Radiation 96
vi Thermodynamics and Statistical Mechanics
Epilogue 97
References 98
6. Electron Gas in a Magnetic Field 100
1. Introduction 100
2. Density Matrix for a Free Electron Gas 100
3. The Energy and Entropy of the System of Fermions 101
4. The Energy of the Electrons in the Crystal Lattice 104
5. Evaluation of Contour Integrals 107
Epilogue 108
References 109
7. Magnetic and Dielectric Materials 111
1. Introduction 111
2. Thermodynamics of Magnetic Materials in a Magnetic Field 112
3. Thermodynamics of Dielectric Materials in an Electric Field 115
4. Dielectric dissipation 117
5. Breakdown 118
6. Maxwell-Wagner relaxation 119
Epilogue 124
References 124
8. Lattice Dynamics 127
1. Introduction 127
2. Periodic Functions of a Reciprocal Lattice 129
3. Reciprocal Lattice 132
4. Vibrational Modes of a Monatomic Lattice 135
5. Linear Monatomic Chain 144
6. Vibrational Modes of A Diatomic Linear Chain 148
7. Properties of the Dynamical Matrix 148
8. Cyclic Boundary for Three-Dimensional Cases 150
9. Born-Von Karman Cyclic Condition 156
Epilogue 157
References 157
9. Condensed Bodies 160
1. Introduction 160
2. Application of Statistical Thermodynamics to Phonons 160
3. Free Energy of Condensed Bodies in the Harmonic Approximation 162
4. Volume Coefficient of Expansion 167
5. Thermal Expansion in Two and Three Dimensions 167
6. Thermal Stress 170
Epilogue 171
References 172
10. Functional Integration in Statistical Physics 174
1. Introduction 174
2. Feynman Path Integrals 175
3. Least Action Principle 175
4. Representation of Transition Amplitude through Functional Integration 178
5. Definition of the S-Matrix 179
6. Transition Probability 180
7. Representation of Matrix Element of Physical Operator through Functional Integral 180
Epilogue 183
References 183
11. Macroscopic Quantum Effects: Superfluid Liquid Helium 186
1. Introduction 186
2. Properties of Liquid Helium 194
3. Superfluidity of Liquid Helium 204
Epilogue 205
References 205
12. Nonideal Classical Gases 207
1. Introduction 207
2. Pair Interactions Approximation 207
3. Van Der Waals Equation 210
4. Completely Ionized Gas 219
Epilogue 229
References 230
Index 231
Alica Robles holds Ph.D. in Fluid Mechanics and Thermodynamics from Technical University, Aiken. She has served as a Guest Lecturer at various universities across America and Europe. She has contributed numerous journals and research papers on the laws of thermodynamics, internal energy, heat, enthalpy and entropy. Her research interest areas are in systems engineering, chemical process modeling and bioengineering.
