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Oxford University Press
Ludwig Boltzmann: The Man Who Trusted Atoms

Ludwig Boltzmann: The Man Who Trusted Atoms

by Carlo Cercignani, Roger Penrose


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Product Details

ISBN-13: 9780198570646
Publisher: Oxford University Press
Publication date: 03/09/2006
Pages: 348
Product dimensions: 9.10(w) x 6.00(h) x 0.90(d)

About the Author

University of Milan

University of Oxford

Table of Contents

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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