# Statistical Mechanics, Kinetic theory, and Stochastic Processes

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Statistical Mechanics, Kinetic Theory, and Stochastic Processes presents the statistical aspects of physics as a "living and dynamic" subject. In order to provide an elementary introduction to kinetic theory, physical systems in which particle-particle interaction can be neglected are considered. Transport phenomena in the free-molecular flow region for gases and the transport of thermal radiation are discussed. Discrete random processes such as random walk, binomial and Poisson distributions, and throwing of dice are studied by means of the characteristic function. Comprised of 11 chapters, this book begins with an introduction to the mass point gas as well as some elementary properties of space and velocity distributions. The discussion then turns to radiation and its interaction with an atom; probability, statistics, and conditional probability; intermolecular interactions; transport phenomena; and statistical thermodynamics. Molecular systems at low densities are also considered, together with non-ideal and real gases; liquids and solids; and stochastic processes, noise, and fluctuations. In particular, the response of atoms and molecules to perturbations and scattering by crystals, liquids, and high-pressure gases are examined. This monograph will be useful for undergraduate students, practitioners, and researchers in physics.

## Table of Contents

Preface

List of Symbols

I Mass Point Gas

1.1 Introduction

1.2 Uniform Space Distributions

1.3 Nonuniform Space Distributions

1.4 Average or Expected Value of Observable Quantities

1.5 Average or Expected Free Paths

1.6 Mass Point Gas

1.7 Effusive Flow of a Mass Point Gas

1.8 Pressure of a Mass Point Gas

1.9 Speed Distribution Function

1.10 Momentum Transfer and Heat Transfer in Free Molecular Flow

1.11 Free Molecular Flow

References

II Radiation

2.1 Introduction

2.2 Electromagnetic Radiation

2.3 Thermal Radiation

2.4 Surface Absorption and Emission of Thermal Radiation

2.5 Radiation Pressure

2.6 Experimental Verification of the Frequency Distribution of Thermal Radiation

2.7 Radiation Temperature

2.8 Interaction of Radiation with an Atom

2.9 Thermal Radiation in Enclosures Containing Matter

2.10 Absorption and Emission of Radiation by Matter

2.11 Motion through Thermal Radiation

References

III Probability, Statistics, And Conditional Probability

3.1 Introduction

3.2 Integral-Valued Random Variables

3.3 Useful Mathematical Formulas

3.4 Random Walk

3.5 Binomial and Poisson Distributions

3.6 Central Limit Theorem

3.7 Conditional Probability

3.8 Physical Processes Continuous in Space and Time

3.9 Random Walk with Absorbing Boundaries

3.10 Some Probability Laws Frequently Encountered in Physics

References

General References

IV Intermolecular Interactions

4.1 Introduction

4.2 Classical Elastic Collisions

4.3 Quantum Aspects of Elastic Collisions

4.4 Cross Sections for Diffusion and Viscosity

4.5 Elastic and Inelastic Binary Collisions

4.6 Inelastic Scattering Cross Section

4.7 Atomic Cross Sections from Atomic Beam Experiments

4.8 Interaction of Molecules with Solid Surfaces

References

V Transport Phenomena

5.1 Introduction

5.2 Elementary Theory of Transport

5.3 Gas Dynamics

5.4 Nonequilibrium Properties of the Distribution Function

5.5 General Transport Equations

5.6 Equilibrium Mixture of Two Gases

5.7 Diffusion

5.8 Sound Waves in Gases

References

VI Statistical Thermodynamics

6.1 Introduction

6.2 Laws of Thermodynamics

6.3 Thermodynamic Functions

6.4 Statistical Physics

References

General References

VII Molecular Systems At Low Densities

7.1 Nearly Ideal Gases

7.2 Photon Gas

7.3 Bose and Fermi Distributions

7.4 Chemical Reactions

7.5 Thermal Ionization and Excitation of Atoms

7.6 Thermodynamic Properties of Heteronuclear Diatomic Molecules

7.7 Homonuclear Diatomic Molecules

7.8 Equipartition Theorem

7.9 Gases at Very High Temperatures

7.10 Paramagnetism

References

VIII Nonideal And Real Gases

8.1 Nonideal Gases

8.2 Cluster Expansion

8.3 Equation of State and Second Virial Coefficient

8.4 Second Virial Coefficients for Classical, Fermi-Dirac, and Bose-Einstein Gases

8.5 Second Virial Coefficient for Molecular Gases with Interaction

8.6 Intermolecular Potentials

8.7 Degenerate Fermi-Dirac Gas—Electrons in Metals and in Very Dense Matter

8.8 Degenerate Bose-Einstein Gas

References

IX Gases, Liquids, And Solids

9.1 Introduction

9.2 Thermodynamic Aspects of Equilibrium between Phases

9.3 Phonon Gas

9.4 Thermodynamic Systems that Are Composed of Different Particles

9.5 The Third Law of Thermodynamics

9.6 Binary Mixtures

9.7 A Combinatorial Problem

9.8 Experimental Critical Points

9.9 Surface-Gas-Phase Equilibrium

References

X Stochastic Processes, Noise, And Fluctuations

10.1 Introduction

10.2 Thermal Motion of a One-Dimensional System

10.3 Random Pulses

10.4 Correlation Function and Spectral Density

10.5 Response of a Simple Harmonic Oscillator to Random Pulses and Thermal Noise

10.6 Correlation Function and Spectral Density for Brownian Motion

10.7 Response of Electrical Circuits to Random Pulses and Thermal Noise

10.8 Fluctuation Dissipation Theorem

10.9 Fluctuations in Thermal Radiation

10.10 General Theory of Fluctuations in Statistical Thermodynamics

10.11 Correlation of Fluctuations and Measurement with Waves

10.12 Nonlinear Physical Systems

10.13 Characteristic Functions for Random Pulses

10.14 Random Processes

References

XI Stochastic Processes In Quantum Systems

11.1 Introduction

11.2 Elementary Theory of Transition Rates

11.3 Density Matrix and the Response of Atoms and Molecules to Perturbations

11.4 Natural Line Width

11.5 Recoilless Emission and the Mössbauer Effect

11.6 Damping and the Golden Rule for Transition Rates

11.7 Theory for Broadening of Spectral Lines in Gases

11.8 Scattering by Crystals, Liquids, and High-Pressure Gases

References

Appendix A: Fundamental Constants

Appendix B: Gaussian Integrals

Index

## Product details

- No. of pages: 618
- Language: English
- Copyright: © Academic Press 1972
- Published: January 1, 1972
- Imprint: Academic Press
- eBook ISBN: 9780323144414

## About the Author

### C.V. Heer

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