- Title Pages
- To my daughter Anna, who helped me through Boltzmann’s dense German
- FOREWORD
- PREFACE
- FIGURE ACKNOWLEDGEMENTS
- Introduction
- 1 A short biography of Ludwig Boltzmann
- 2 Physics before Boltzmann
- 3 Kinetic theory before Boltzmann
- 4 The Boltzmann equation
- 5 Time irreversibility and the H-theorem
- 6 Boltzmann’s relation and the statistical interpretation of entropy
- 7 Boltzmann, Gibbs, and equilibrium statistical mechanics
- 8 The problem of polyatomic molecules
- 9 Boltzmann’s contributions to other branches of physics
- 10 Boltzmann as a philosopher
- 11 Boltzmann and his contemporaries
- 12 The influence of Boltzmann’s ideas on the science and technology of the twentieth century
- 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 H-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
- Index
Boltzmann’s contributions to other branches of physics
Boltzmann’s contributions to other branches of physics
- Chapter:
- (p.160) 9 Boltzmann’s contributions to other branches of physics
- Source:
- Ludwig Boltzmann
- Author(s):
CARLO CERCIGNANI
- Publisher:
- Oxford University Press
Ludwig Boltzmann's scientific activities were mainly devoted to statistical mechanics: in large measure to kinetic theory, but he also founded the formalism of equilibrium statistical mechanics for systems of a general kind, the paternity of which is usually, in a more or less explicit way, attributed to Josiah Willard Gibbs. About half of Boltzmann's publications deal with contributions to diverse areas, ranging over the fields of physics, chemistry, mathematics, and philosophy. This chapter examines this secondary but not negligible aspect of Boltzmann's scientific activity. Having fathomed the meaning of the theory and implications of James Clerk Maxwell's equations and in particular the unification between electromagnetism and optics, Boltzmann wrote his first paper on electrodynamics. He also studied the law that according to the Maxwell picture related the dielectric constant and the refractive index of a given material. This chapter looks at Boltzmann's contributions regarding Maxwell's theory of electromagnetism, hereditary mechanics, theoretical physics, mathematics, and foundations of mechanics.
Keywords: optics, theoretical physics, electromagnetism, James Clerk Maxwell, optics, hereditary mechanics, mathematics, mechanics, dielectric constant
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- Title Pages
- To my daughter Anna, who helped me through Boltzmann’s dense German
- FOREWORD
- PREFACE
- FIGURE ACKNOWLEDGEMENTS
- Introduction
- 1 A short biography of Ludwig Boltzmann
- 2 Physics before Boltzmann
- 3 Kinetic theory before Boltzmann
- 4 The Boltzmann equation
- 5 Time irreversibility and the H-theorem
- 6 Boltzmann’s relation and the statistical interpretation of entropy
- 7 Boltzmann, Gibbs, and equilibrium statistical mechanics
- 8 The problem of polyatomic molecules
- 9 Boltzmann’s contributions to other branches of physics
- 10 Boltzmann as a philosopher
- 11 Boltzmann and his contemporaries
- 12 The influence of Boltzmann’s ideas on the science and technology of the twentieth century
- 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 H-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
- Index