### Available:*

Library | Call Number | Material Type | Home Location | Status | Item Holds |
---|---|---|---|---|---|

Searching... | QC16.B64 C47 1998 | Adult Non-Fiction | Central Closed Stacks | Searching... | Searching... |

### On Order

### Summary

### Summary

The book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th to 20th century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantialpart of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies isdocumented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific revolution, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientificrevolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved; others are still at the level of likely but unproven conjectures. The main text of this biography is writtenalmost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject.

### Author Notes

Carlo Cercignani is a Professor of Theoretical Mechanics at Politecnico di Milano.

### Table of Contents

Figure acknowledgements | p. xvii |

Introduction | p. 1 |

1 A short biography of Ludwig Boltzmann | p. 5 |

1.1 Youth and happy years | p. 5 |

1.2 The crisis | p. 20 |

1.3 Restlessness | p. 22 |

1.4 Scientific debates and travels | p. 26 |

1.5 The tragic fate of a great scientist | p. 34 |

1.6 Boltzmann as a teacher | p. 37 |

1.7 Boltzmann and inventions | p. 38 |

1.8 Ludwig Boltzmann and his times | p. 39 |

1.9 A poem by Ludwig Boltzmann | p. 46 |

1.10 Boltzmann's personality | p. 48 |

2 Physics before Boltzmann | p. 50 |

2.1 From Galileo and Newton to the early atomic theories | p. 50 |

2.2 The first connections between heat and mechanical energy | p. 56 |

2.3 The springtime of thermodynamics | p. 59 |

2.4 Electricity and magnetism | p. 65 |

3 Kinetic theory before Boltzmann | p. 71 |

3.1 Early kinetic theories | p. 71 |

3.2 The beginnings of modern kinetic theory and the problem of justifying the Second Law | p. 80 |

4 The Boltzmann equation | p. 86 |

4.1 Irreversibility and kinetic theory | p. 86 |

4.2 The great paper of 1872 | p. 88 |

4.3 A critique of Boltzmann's approach | p. 93 |

5 Time irreversibility and the H-theorem | p. 96 |

5.1 Introduction | p. 96 |

5.2 Loschmidt's paradox | p. 97 |

5.3 Poincare's recurrence and Zermelo's paradox | p. 100 |

5.4 The physical and mathematical resolution of the paradoxes | p. 102 |

5.5 Timers arrow and the expanding universe | p. 109 |

5.6 Is irreversibility objective or subjective? | p. 112 |

5.7 Concluding remarks | p. 118 |

6 Boltzmann's relation and the statistical interpretation of entropy | p. 120 |

6.1 The probabilistic interpretation of thermodynamics | p. 120 |

6.2 Explicit use of probability for a gas with discrete energies | p. 121 |

6.3 Energy is continuous | p. 125 |

6.4 The so-called H-curve | p. 129 |

7 Boltzmann, Gibbs, and equilibrium statistical mechanics | p. 134 |

7.1 Introduction | p. 134 |

7.2 A great American scientist of the nineteenth century: J.W. Gibbs | p. 135 |

7.3 Why is statistical mechanics usually attributed to Gibbs and not to Boltzmann? | p. 140 |

7.4 Gibbs's treatise | p. 142 |

7.5 French scientists on statistical mechanics | p. 145 |

7.6 The problem of trend to equilibrium and ergodic theory | p. 146 |

7.7 Planck and statistical mechanics | p. 150 |

8 The problem of polyatomic molecules | p. 153 |

8.1 The problem of specific heats | p. 153 |

8.2 The H-theorem for polyatomic molecules | p. 154 |

8.3 Specific heats again | p. 155 |

8.4 Boltzmann's ideas on specific heats, and twentieth century contributions | p. 157 |

9 Boltzmann's contributions to other branches of physics | p. 160 |

9.1 Boltzmann's testing of Maxwell's theory of electromagnetism | p. 160 |

9.2 Boltzmann lays the foundations of hereditary mechanics | p. 161 |

9.3 Back to electromagnetism | p. 162 |

9.4 A true pearl of theoretical physics | p. 163 |

9.5 Mathematics and foundations of mechanics | p. 164 |

10 Boltzmann as a philosopher | p. 170 |

10.1 A realist, but not a naive one | p. 170 |

10.2 Laws of thought and scientific concepts | p. 177 |

10.3 Ethics, aesthetics, religion | p. 181 |

10.4 Philosophy of science | p. 184 |

10.5 Boltzmann's views on scientific revolutions | p. 189 |

10.6 Boltzmann's education in philosophy | p. 191 |

10.7 Did Boltzmann abandon realism? | p. 192 |

11 Boltzmann and his contemporaries | p. 198 |

11.1 The contacts between Boltzmann and his colleagues | p. 198 |

11.2 Maxwell | p. 198 |

11.3 Lorentz | p. 200 |

11.4 Boltzmann and the energetists | p. 202 |

11.5 Planck | p. 210 |

11.6 Students and younger colleagues | p. 211 |

12 The influence of Boltzmann's ideas on the science and technology of the twentieth century | p. 214 |

12.1 Brownian motion | p. 214 |

12.2 Enter Einstein | p. 215 |

12.3 Black-body radiation | p. 217 |

12.4 Einstein again | p. 220 |

12.5 The role of Boltzmann's ideas during the twentieth century | p. 223 |

Epilogue | p. 226 |

Chronology | p. 227 |

"A German professor's journey into Eldorado" | p. 231 |

Appendices | p. 251 |

A 3.1 Calculation of pressure in a rarefied gas | p. 251 |

A 4.1 The Liouville equation | p. 255 |

A 4.2 Calculation of the effect of collisions of one particle with another | p. 259 |

A 4.3 The BBGKY hierarchy | p. 261 |

A 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equation | p. 264 |

A 4.5 The Boltzmann equation in the homogeneous isotropic case | p. 266 |

A 5.1 Collision-invariants | p. 267 |

A 5.2 Boltzmann's inequality and the Maxwell distribution | p. 271 |

A 5.3 The H-theorem | p. 273 |

A 5.4 The hourglass model | p. 277 |

A 6.1 Likelihood of a distribution | p. 280 |

A 7.1 The canonical distribution for equilibrium states | p. 283 |

A 8.1 The H-theorem for classical polyatomic molecules | p. 287 |

A 8.2 The equipartition problem | p. 291 |

A 9.1 The Stefan-Boltzmann law | p. 294 |

A 9.2 Wien's law | p. 295 |

References | p. 297 |

Index | p. 319 |