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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
- <i>Index</i>

# (p.255) Appendix 4.1 The Liouville equation

# (p.255) Appendix 4.1 The Liouville equation

- Source:
- Ludwig Boltzmann
- Publisher:
- Oxford University Press

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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
- <i>Index</i>