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Copyright: 2000

Publisher: University Science Books

Published: 2000

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Copyright: 2000

Publisher: University Science Books

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With this edition, University Science Books becomes the publisher of both my Statistical Thermodynamics and Statistical Mechanics books. I would like to thank the publisher, Bruce Armbruster, for his continual commitment to

quality textbook publishing in the sciences.

Statistical Mechanics is the extended version of my earlier text, Statistical Thermodynamics. The present volume is intended primarily for a two-semester course or for a second one-semester course in statistical mechanics. Whereas Statistical Thermodynamics deals principally with equilibrium systems whose particles are either independent or effectively

independent, Statistical Mechanics treats equilibrium systems whose particles are strongly interacting as well as nonequilibrium systems. The first twelve chapters of this book also form the first chapters in Statistical Thermodynamics, while the next ten chapters, 13-22, appear only in Statistical Mechanics. Chapter 13 deals with the radial distribution function approach to liquids, and Chapter 14 is a fairly detailed discussion of statistical mechanical perturbation theories of liquids. These theories were developed in the late 1960s and early 1970s and have brought the numerical calculation of the thermodynamic properties of simple dense fluids to a practical level. A number of the problems at the end of the Chapter 14 require the student to calculate such properties and compare the results to experimental data. Chapter 15, on ionic solutions, is the last chapter on

equilibrium systems. Section 15-2 is an introduction to advances in ionic solution theory that were developed in the 1970s

and that now allow one to calculate the thermodynamic properties of simple ionic solutions up to concentrations of 2 molar.

Chapters 16-22 treat systems that are not in equilibrium. Chapters 16 and 17 are meant to be somewhat of a review, although admittedly much of the material, particularly in Chapter 17, will be new. Nevertheless, these two chapters do serve as a background for the rest. Chapter 18 presents the rigorous kinetic theory of gases as formulated through the Boltzmann

equation, the famous integro-differential equation whose solution gives the nonequilibrium distribution of a molecule in velocity space. The long-time or equilibrium solution of the Boltzmann equation is the well-known Maxwell-Boltzmann distribution (Chapter 7). Being an integro-differential equation, it is not surprising that its solution is fairly involved. We only outline the standard method of solution, called the Chapman-Enskog method, in Section 19-1, and the next two sections are a practical

calculation of the transport properties of gases. In the last section of Chapter 19 we discuss Enskog's ad hoc extension of the Boltzmann equation to dense hard-sphere fluids. Chapter 20, which presents the Langevin equation and the Fokker-Planck equation, again is somewhat of a digression but does serve as a background to Chapters 21 and 22.

The 1950s saw the beginning of the development of a new approach to transport processes that has grown into one of the most active and fruitful areas of nonequilibrium statistical mechanics. This work was initiated by Green and Kubo, who showed that the phenomenological coefficients describing many transport processes and time-dependent phenomena in general could be

written as integrals over a certain type of function called a time-correlation function. The time-correlation function associated with some particular process is in a sense the analog of the partition function for equilibrium systems. Although both are difficult to evaluate exactly, the appropriate properties of the system of interest can be formally expressed in terms of these functions, and they serve as basic starting points for computationally convenient approximations. Before the development of the time-correlation function formalism, there was no single unifying approach to nonequilibrium statistical mechanics such as Gibbs had given to equilibrium statistical mechanics.

Chapters 21 and 22, two long chapters, introduce the time-correlation function approach. We have chosen to introduce the time-correlation function formalism through the absorption of electromagnetic radiation by a system of molecules since the application is of general interest and the derivation of the key formulas is quite pedagogical and requires no special techniques. After presenting a similar application to light scattering, we then develop the formalism in a more general way and apply the general formalism to dielectric relaxation, thermal transport, neutron scattering, light scattering, and several others.

Eleven appendixes are also included to supplement the textual material.

The intention here is to present a readable introduction to the topics covered rather than a rigorous, formal development. In addition, a great number of problems is included at the end of each chapter in order either to increase the student's understanding of the material or to introduce him or her to selected extensions.

As this printing goes to press, we are beginning to plan a new edition of Statistical Mechanics. We would be grateful for any and all feedback from loyal users intended to help us shape the next edition of this text.

**McQuarrie, Donald A. : University of California, Davis**

**1. Introduction and Review 2. The Canonical Ensemble 3. Other Ensembles and Fluctuations 4. Boltzmann Statistics, Fermi-Dirac Statistics, and Bose-Einstein Statistics 5. Ideal Monatomic Gas 6. Ideal Diatomic Gas 7. Classical Statistical Mechanics 8. Ideal Polyatomic Gas 9. Chemical Equilibrium 10. Quantum Statistics 11. Crystals 12. Imperfect Gases 13. Distribution Functions in Classical Monatomic Liquids 14. Perturbation Theories of Liquids 15. Solutions of Strong Electrolytes 16. Kinetic Theory of Gases and Molecular Collisions 17. Continuum Mechanics 18. Kinetic Theory of Gases and the Boltzmann Equation 19. Transport Processes in Dilute Gases 20. Theory of Brownian Motion 21. The Time-Correlation Function Formalism, I 22. The Time-Correlation Function Formalism, II **Appendix A. Values of Some Physical Constants and Energy Conversion Factors

Appendix B. Fourier Integrals and the Dirac Delta Function

Appendix C. Debye Heat Capacity Function

Appendix D. Hard-Sphere Radial Distribution Function

Appendix E. Tables for the m-6-8 Potential

Appendix F. Derivation of the Golden Rule of Perturbation Theory

Appendix G. The Dirac BRA and KET Notation

Appendix H. The Heisenberg Time-Dependent Representation

Appendix I. The Poynting Flux Vector

Appendix J. The Radiation Emitted by an Oscillating Dipole

Appendix K. Dielectric Constant and Absorption

Index

Summary

With this edition, University Science Books becomes the publisher of both my Statistical Thermodynamics and Statistical Mechanics books. I would like to thank the publisher, Bruce Armbruster, for his continual commitment to

quality textbook publishing in the sciences.

Statistical Mechanics is the extended version of my earlier text, Statistical Thermodynamics. The present volume is intended primarily for a two-semester course or for a second one-semester course in statistical mechanics. Whereas Statistical Thermodynamics deals principally with equilibrium systems whose particles are either independent or effectively

independent, Statistical Mechanics treats equilibrium systems whose particles are strongly interacting as well as nonequilibrium systems. The first twelve chapters of this book also form the first chapters in Statistical Thermodynamics, while the next ten chapters, 13-22, appear only in Statistical Mechanics. Chapter 13 deals with the radial distribution function approach to liquids, and Chapter 14 is a fairly detailed discussion of statistical mechanical perturbation theories of liquids. These theories were developed in the late 1960s and early 1970s and have brought the numerical calculation of the thermodynamic properties of simple dense fluids to a practical level. A number of the problems at the end of the Chapter 14 require the student to calculate such properties and compare the results to experimental data. Chapter 15, on ionic solutions, is the last chapter on

equilibrium systems. Section 15-2 is an introduction to advances in ionic solution theory that were developed in the 1970s

and that now allow one to calculate the thermodynamic properties of simple ionic solutions up to concentrations of 2 molar.

Chapters 16-22 treat systems that are not in equilibrium. Chapters 16 and 17 are meant to be somewhat of a review, although admittedly much of the material, particularly in Chapter 17, will be new. Nevertheless, these two chapters do serve as a background for the rest. Chapter 18 presents the rigorous kinetic theory of gases as formulated through the Boltzmann

equation, the famous integro-differential equation whose solution gives the nonequilibrium distribution of a molecule in velocity space. The long-time or equilibrium solution of the Boltzmann equation is the well-known Maxwell-Boltzmann distribution (Chapter 7). Being an integro-differential equation, it is not surprising that its solution is fairly involved. We only outline the standard method of solution, called the Chapman-Enskog method, in Section 19-1, and the next two sections are a practical

calculation of the transport properties of gases. In the last section of Chapter 19 we discuss Enskog's ad hoc extension of the Boltzmann equation to dense hard-sphere fluids. Chapter 20, which presents the Langevin equation and the Fokker-Planck equation, again is somewhat of a digression but does serve as a background to Chapters 21 and 22.

The 1950s saw the beginning of the development of a new approach to transport processes that has grown into one of the most active and fruitful areas of nonequilibrium statistical mechanics. This work was initiated by Green and Kubo, who showed that the phenomenological coefficients describing many transport processes and time-dependent phenomena in general could be

written as integrals over a certain type of function called a time-correlation function. The time-correlation function associated with some particular process is in a sense the analog of the partition function for equilibrium systems. Although both are difficult to evaluate exactly, the appropriate properties of the system of interest can be formally expressed in terms of these functions, and they serve as basic starting points for computationally convenient approximations. Before the development of the time-correlation function formalism, there was no single unifying approach to nonequilibrium statistical mechanics such as Gibbs had given to equilibrium statistical mechanics.

Chapters 21 and 22, two long chapters, introduce the time-correlation function approach. We have chosen to introduce the time-correlation function formalism through the absorption of electromagnetic radiation by a system of molecules since the application is of general interest and the derivation of the key formulas is quite pedagogical and requires no special techniques. After presenting a similar application to light scattering, we then develop the formalism in a more general way and apply the general formalism to dielectric relaxation, thermal transport, neutron scattering, light scattering, and several others.

Eleven appendixes are also included to supplement the textual material.

The intention here is to present a readable introduction to the topics covered rather than a rigorous, formal development. In addition, a great number of problems is included at the end of each chapter in order either to increase the student's understanding of the material or to introduce him or her to selected extensions.

As this printing goes to press, we are beginning to plan a new edition of Statistical Mechanics. We would be grateful for any and all feedback from loyal users intended to help us shape the next edition of this text.

Author Bio

**McQuarrie, Donald A. : University of California, Davis**

Table of Contents

**1. Introduction and Review 2. The Canonical Ensemble 3. Other Ensembles and Fluctuations 4. Boltzmann Statistics, Fermi-Dirac Statistics, and Bose-Einstein Statistics 5. Ideal Monatomic Gas 6. Ideal Diatomic Gas 7. Classical Statistical Mechanics 8. Ideal Polyatomic Gas 9. Chemical Equilibrium 10. Quantum Statistics 11. Crystals 12. Imperfect Gases 13. Distribution Functions in Classical Monatomic Liquids 14. Perturbation Theories of Liquids 15. Solutions of Strong Electrolytes 16. Kinetic Theory of Gases and Molecular Collisions 17. Continuum Mechanics 18. Kinetic Theory of Gases and the Boltzmann Equation 19. Transport Processes in Dilute Gases 20. Theory of Brownian Motion 21. The Time-Correlation Function Formalism, I 22. The Time-Correlation Function Formalism, II **Appendix A. Values of Some Physical Constants and Energy Conversion Factors

Appendix B. Fourier Integrals and the Dirac Delta Function

Appendix C. Debye Heat Capacity Function

Appendix D. Hard-Sphere Radial Distribution Function

Appendix E. Tables for the m-6-8 Potential

Appendix F. Derivation of the Golden Rule of Perturbation Theory

Appendix G. The Dirac BRA and KET Notation

Appendix H. The Heisenberg Time-Dependent Representation

Appendix I. The Poynting Flux Vector

Appendix J. The Radiation Emitted by an Oscillating Dipole

Appendix K. Dielectric Constant and Absorption

Index

Publisher Info

Publisher: University Science Books

Published: 2000

International: No

Published: 2000

International: No

quality textbook publishing in the sciences.

Statistical Mechanics is the extended version of my earlier text, Statistical Thermodynamics. The present volume is intended primarily for a two-semester course or for a second one-semester course in statistical mechanics. Whereas Statistical Thermodynamics deals principally with equilibrium systems whose particles are either independent or effectively

independent, Statistical Mechanics treats equilibrium systems whose particles are strongly interacting as well as nonequilibrium systems. The first twelve chapters of this book also form the first chapters in Statistical Thermodynamics, while the next ten chapters, 13-22, appear only in Statistical Mechanics. Chapter 13 deals with the radial distribution function approach to liquids, and Chapter 14 is a fairly detailed discussion of statistical mechanical perturbation theories of liquids. These theories were developed in the late 1960s and early 1970s and have brought the numerical calculation of the thermodynamic properties of simple dense fluids to a practical level. A number of the problems at the end of the Chapter 14 require the student to calculate such properties and compare the results to experimental data. Chapter 15, on ionic solutions, is the last chapter on

equilibrium systems. Section 15-2 is an introduction to advances in ionic solution theory that were developed in the 1970s

and that now allow one to calculate the thermodynamic properties of simple ionic solutions up to concentrations of 2 molar.

Chapters 16-22 treat systems that are not in equilibrium. Chapters 16 and 17 are meant to be somewhat of a review, although admittedly much of the material, particularly in Chapter 17, will be new. Nevertheless, these two chapters do serve as a background for the rest. Chapter 18 presents the rigorous kinetic theory of gases as formulated through the Boltzmann

equation, the famous integro-differential equation whose solution gives the nonequilibrium distribution of a molecule in velocity space. The long-time or equilibrium solution of the Boltzmann equation is the well-known Maxwell-Boltzmann distribution (Chapter 7). Being an integro-differential equation, it is not surprising that its solution is fairly involved. We only outline the standard method of solution, called the Chapman-Enskog method, in Section 19-1, and the next two sections are a practical

calculation of the transport properties of gases. In the last section of Chapter 19 we discuss Enskog's ad hoc extension of the Boltzmann equation to dense hard-sphere fluids. Chapter 20, which presents the Langevin equation and the Fokker-Planck equation, again is somewhat of a digression but does serve as a background to Chapters 21 and 22.

The 1950s saw the beginning of the development of a new approach to transport processes that has grown into one of the most active and fruitful areas of nonequilibrium statistical mechanics. This work was initiated by Green and Kubo, who showed that the phenomenological coefficients describing many transport processes and time-dependent phenomena in general could be

written as integrals over a certain type of function called a time-correlation function. The time-correlation function associated with some particular process is in a sense the analog of the partition function for equilibrium systems. Although both are difficult to evaluate exactly, the appropriate properties of the system of interest can be formally expressed in terms of these functions, and they serve as basic starting points for computationally convenient approximations. Before the development of the time-correlation function formalism, there was no single unifying approach to nonequilibrium statistical mechanics such as Gibbs had given to equilibrium statistical mechanics.

Chapters 21 and 22, two long chapters, introduce the time-correlation function approach. We have chosen to introduce the time-correlation function formalism through the absorption of electromagnetic radiation by a system of molecules since the application is of general interest and the derivation of the key formulas is quite pedagogical and requires no special techniques. After presenting a similar application to light scattering, we then develop the formalism in a more general way and apply the general formalism to dielectric relaxation, thermal transport, neutron scattering, light scattering, and several others.

Eleven appendixes are also included to supplement the textual material.

The intention here is to present a readable introduction to the topics covered rather than a rigorous, formal development. In addition, a great number of problems is included at the end of each chapter in order either to increase the student's understanding of the material or to introduce him or her to selected extensions.

As this printing goes to press, we are beginning to plan a new edition of Statistical Mechanics. We would be grateful for any and all feedback from loyal users intended to help us shape the next edition of this text.

**McQuarrie, Donald A. : University of California, Davis**

**1. Introduction and Review 2. The Canonical Ensemble 3. Other Ensembles and Fluctuations 4. Boltzmann Statistics, Fermi-Dirac Statistics, and Bose-Einstein Statistics 5. Ideal Monatomic Gas 6. Ideal Diatomic Gas 7. Classical Statistical Mechanics 8. Ideal Polyatomic Gas 9. Chemical Equilibrium 10. Quantum Statistics 11. Crystals 12. Imperfect Gases 13. Distribution Functions in Classical Monatomic Liquids 14. Perturbation Theories of Liquids 15. Solutions of Strong Electrolytes 16. Kinetic Theory of Gases and Molecular Collisions 17. Continuum Mechanics 18. Kinetic Theory of Gases and the Boltzmann Equation 19. Transport Processes in Dilute Gases 20. Theory of Brownian Motion 21. The Time-Correlation Function Formalism, I 22. The Time-Correlation Function Formalism, II **Appendix A. Values of Some Physical Constants and Energy Conversion Factors

Appendix B. Fourier Integrals and the Dirac Delta Function

Appendix C. Debye Heat Capacity Function

Appendix D. Hard-Sphere Radial Distribution Function

Appendix E. Tables for the m-6-8 Potential

Appendix F. Derivation of the Golden Rule of Perturbation Theory

Appendix G. The Dirac BRA and KET Notation

Appendix H. The Heisenberg Time-Dependent Representation

Appendix I. The Poynting Flux Vector

Appendix J. The Radiation Emitted by an Oscillating Dipole

Appendix K. Dielectric Constant and Absorption

Index