- Title Pages
- <i>To my daughter Anna, who helped me through Boltzmann’s dense German</i>
- Foreword
- Preface
- Figure Acknowledgements
- <i>Introduction</i>
- 1 <i>A short biography of Ludwig Boltzmann</i>
- 2 <i>Physics before Boltzmann</i>
- 3 <i>Kinetic theory before Boltzmann</i>
- 4 <i>The Boltzmann equation</i>
- 5 <i>Time irreversibility and the H-theorem</i>
- 6 <i>Boltzmann’s relation and the statistical interpretation of entropy</i>
- 7 <i>Boltzmann, Gibbs, and equilibrium statistical mechanics</i>
- 8 <i>The problem of polyatomic molecules</i>
- 9 <i>Boltzmann’s contributions to other branches of physics</i>
- 10 <i>Boltzmann as a philosopher</i>
- 11 <i>Boltzmann and his contemporaries</i>
- 12 <i>The influence of Boltzmann’s ideas on the science and technology of the twentieth century</i>
- Epilogue
- CHRONOLOGY
- “A German professor’s journey into Eldorado”*
- Appendix 3.1 Calculation of pressure in a rarefied gas
- Appendix 4.1 The Liouville equation
- Appendix 4.2 Calculation of the effect of collisions of one particle with another
- Appendix 4.3 The BBGKY hierarchy
- Appendix 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equation
- Appendix 4.5 The Boltzmann equation in the homogeneous isotropic case
- Appendix 5.1 Collision-invariants
- Appendix 5.2 Boltzmann’s inequality and the Maxwellian distribution
- Appendix 5.3 The H-theorem
- Appendix 5.4 The hourglass model
- Appendix 6.1 Likelihood of a distribution
- Appendix 7.1 The canonical distribution for equilibrium states
- Appendix 8.1 The <i>H</i>-theorem for classical polyatomic molecules
- Appendix 8.2 The equipartition problem
- Appendix 9.1 The Stefan–Boltzmann law
- Appendix 9.2 Wien’s law
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
- Epilogue
- <i>Index</i>
Kinetic theory before Boltzmann
Kinetic theory before Boltzmann
- Chapter:
- (p.71) 3 Kinetic theory before Boltzmann
- Source:
- Ludwig Boltzmann
- Author(s):
CARLO CERCIGNANI
- Publisher:
- Oxford University Press
The first atomic theory is credited to Democritus of Abdera, who lived in the 5th century BC. The actual development of the kinetic theory of gases accordingly took place much later, in the 19th century. With his transfer equations, James Clerk Maxwell had come very close to an evolution equation for the distribution function, but this last step must beyond any doubt be credited to Ludwig Boltzmann. The equation under consideration is usually called the Boltzmann equation, but sometimes the Maxwell-Boltzmann equation. Rudolf Clausius took kinetic theory to a mature stage with the explicit recognition that thermal energy is but the kinetic energy of the random motion of the molecules and the explanation of the first law of thermodynamics in kinetic terms. In any case there remained the important unsolved problem of deducing the second law of thermodynamics, the basis of the modern idea of irreversibility in physical processes.
Keywords: kinetic theory, atomic theory, Democritus of Abdera, James Clerk Maxwell, Rudolf Clausius, Boltzmann equation, molecules, irreversibility, thermal energy, thermodynamics
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- Title Pages
- <i>To my daughter Anna, who helped me through Boltzmann’s dense German</i>
- Foreword
- Preface
- Figure Acknowledgements
- <i>Introduction</i>
- 1 <i>A short biography of Ludwig Boltzmann</i>
- 2 <i>Physics before Boltzmann</i>
- 3 <i>Kinetic theory before Boltzmann</i>
- 4 <i>The Boltzmann equation</i>
- 5 <i>Time irreversibility and the H-theorem</i>
- 6 <i>Boltzmann’s relation and the statistical interpretation of entropy</i>
- 7 <i>Boltzmann, Gibbs, and equilibrium statistical mechanics</i>
- 8 <i>The problem of polyatomic molecules</i>
- 9 <i>Boltzmann’s contributions to other branches of physics</i>
- 10 <i>Boltzmann as a philosopher</i>
- 11 <i>Boltzmann and his contemporaries</i>
- 12 <i>The influence of Boltzmann’s ideas on the science and technology of the twentieth century</i>
- Epilogue
- CHRONOLOGY
- “A German professor’s journey into Eldorado”*
- Appendix 3.1 Calculation of pressure in a rarefied gas
- Appendix 4.1 The Liouville equation
- Appendix 4.2 Calculation of the effect of collisions of one particle with another
- Appendix 4.3 The BBGKY hierarchy
- Appendix 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equation
- Appendix 4.5 The Boltzmann equation in the homogeneous isotropic case
- Appendix 5.1 Collision-invariants
- Appendix 5.2 Boltzmann’s inequality and the Maxwellian distribution
- Appendix 5.3 The H-theorem
- Appendix 5.4 The hourglass model
- Appendix 6.1 Likelihood of a distribution
- Appendix 7.1 The canonical distribution for equilibrium states
- Appendix 8.1 The <i>H</i>-theorem for classical polyatomic molecules
- Appendix 8.2 The equipartition problem
- Appendix 9.1 The Stefan–Boltzmann law
- Appendix 9.2 Wien’s law
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
- Epilogue
- <i>Index</i>