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Figure acknowledgements xvii
Introduction 1
A short biography of Ludwig Boltzmann 5
Youth and happy years 5
The crisis 20
Restlessness 22
Scientific debates and travels 26
The tragic fate of a great scientist 34
Boltzmann as a teacher 37
Boltzmann and inventions 38
Ludwig Boltzmann and his times 39
A poem by Ludwig Boltzmann 46
Boltzmann's personality 48
Physics before Boltzmann 50
From Galileo and Newton to the early atomic theories 50
The first connections between heat and mechanical energy 56
The springtime of thermodynamics 59
Electricity and magnetism 65
Kinetic theory before Boltzmann 71
Early kinetic theories 71
The beginnings of modern kinetic theory and the problem of justifying the Second Law 80
The Boltzmann equation 86
Irreversibility and kinetic theory 86
The great paper of 1872 88
A critique of Boltzmann's approach 93
Time irreversibility and the H-theorem 96
Introduction 96
Loschmidt's paradox 97
Poincare's recurrence and Zermelo's paradox 100
The physical and mathematical resolution of the paradoxes 102
Timers arrow and the expanding universe 109
Is irreversibility objective or subjective? 112
Concluding remarks 118
Boltzmann's relation and the statistical interpretation of entropy 120
The probabilistic interpretation of thermodynamics 120
Explicit use of probability for a gas with discrete energies 121
Energy is continuous 125
The so-called H-curve 129
Boltzmann, Gibbs, and equilibrium statistical mechanics 134
Introduction 134
A great American scientist of the nineteenth century: J.W. Gibbs 135
Why is statistical mechanics usually attributed to Gibbs and not to Boltzmann? 140
Gibbs's treatise 142
French scientists on statistical mechanics 145
The problem of trend to equilibrium and ergodic theory 146
Planck and statistical mechanics 150
The problem of polyatomic molecules 153
The problem of specific heats 153
The H-theorem for polyatomic molecules 154
Specific heats again 155
Boltzmann's ideas on specific heats, and twentieth century contributions 157
Boltzmann's contributions to other branches of physics 160
Boltzmann's testing of Maxwell's theory of electromagnetism 160
Boltzmann lays the foundations of hereditary mechanics 161
Back to electromagnetism 162
A true pearl of theoretical physics 163
Mathematics and foundations of mechanics 164
Boltzmann as a philosopher 170
A realist, but not a naive one 170
Laws of thought and scientific concepts 177
Ethics, aesthetics, religion 181
Philosophy of science 184
Boltzmann's views on scientific revolutions 189
Boltzmann's education in philosophy 191
Did Boltzmann abandon realism? 192
Boltzmann and his contemporaries 198
The contacts between Boltzmann and his colleagues 198
Maxwell 198
Lorentz 200
Boltzmann and the energetists 202
Planck 210
Students and younger colleagues 211
The influence of Boltzmann's ideas on the science and technology of the twentieth century 214
Brownian motion 214
Enter Einstein 215
Black-body radiation 217
Einstein again 220
The role of Boltzmann's ideas during the twentieth century 223
Epilogue 226
Chronology 227
"A German professor's journey into Eldorado" 231
Appendices 251
Calculation of pressure in a rarefied gas 251
The Liouville equation 255
Calculation of the effect of collisions of one particle with another 259
The BBGKY hierarchy 261
The Boltzmann hierarchy and its relation to the Boltzmann equation 264
The Boltzmann equation in the homogeneous isotropic case 266
Collision-invariants 267
Boltzmann's inequality and the Maxwell distribution 271
The H-theorem 273
The hourglass model 277
Likelihood of a distribution 280
The canonical distribution for equilibrium states 283
The H-theorem for classical polyatomic molecules 287
The equipartition problem 291
The Stefan-Boltzmann law 294
Wien's law 295
References 297
Index 319
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