- 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>
Boltzmann’s relation and the statistical interpretation of entropy
Boltzmann’s relation and the statistical interpretation of entropy
- Chapter:
- (p.120) 6 Boltzmann’s relation and the statistical interpretation of entropy
- Source:
- Ludwig Boltzmann
- Author(s):
CARLO CERCIGNANI
- Publisher:
- Oxford University Press
Ludwig Boltzmann first used probabilistic arguments in his answer to Johann Loschmidt's objection to his Boltzmann equation and his assumptions about entropy in the H-theorem. Up to that moment, although he mentioned probability in his papers, Boltzmann seemed to think that the distribution function was a way of utilising the techniques of mathematical analysis in order to count the actual numbers of molecules, and no hidden probabilistic assumption was contained in his arguments. If Boltzmann had already begun to hint at the important role of probability in 1871, the priority in stressing the necessity of a statistical interpretation of the second law of thermodynamics must certainly be credited to James Clerk Maxwell because of his invention of the demon now named after him. This chapter discusses the probabilistic interpretation of thermodynamics, explicit use of probability for a gas with discrete energies, energy as a continuous phemonenon, and the so-called H-curve.
Keywords: H-theorem, probability, entropy, H-curve, Boltzmann equation, distribution function, James Clerk Maxwell, molecules, thermodynamics, energy
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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>