Ludwig Boltzmann The Man Who Trusted Atoms

by Cercignani, Carlo; Penrose, Roger

• ISBN13: 9780198570646
• ISBN10: 0198570643
• Format: Paperback
• Copyright: 2006-03-09
• Publisher: Oxford University Press

Summary

Ludwig Boltzmann arguably played the key role in establishing that submicroscopic structures underlie the ordinary world. He had a tremendous impact on late 19th-century and early 20th-century physics, and he anticipated many contemporary ideas, including

Author Biography

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

Table of Contents

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