Figure acknowledgements |
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xvii | |
Introduction |
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1 | (4) |
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1 A short biography of Ludwig Boltzmann |
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5 | (45) |
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1.1 Youth and happy years |
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5 | (15) |
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20 | (2) |
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22 | (4) |
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1.4 Scientific debates and travels |
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26 | (8) |
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1.5 The tragic fate of a great scientist |
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34 | (3) |
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1.6 Boltzmann as a teacher |
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37 | (1) |
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1.7 Boltzmann and inventions |
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38 | (1) |
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1.8 Ludwig Boltzmann and his times |
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39 | (7) |
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1.9 A poem by Ludwig Boltzmann |
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46 | (2) |
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1.10 Boltzmann's personality |
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48 | (2) |
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2 Physics before Boltzmann |
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50 | (21) |
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2.1 From Galileo and Newton to the early atomic theories |
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50 | (6) |
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2.2 The first connections between heat and mechanical energy |
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56 | (3) |
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2.3 The springtime of thermodynamics |
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59 | (6) |
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2.4 Electricity and magnetism |
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65 | (6) |
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3 Kinetic theory before Boltzmann |
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71 | (15) |
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3.1 Early kinetic theories |
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71 | (9) |
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3.2 The beginnings of modern kinetic theory and the problem of justifying the Second Law |
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80 | (6) |
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86 | (10) |
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4.1 Irreversibility and kinetic theory |
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86 | (2) |
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4.2 The great paper of 1872 |
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88 | (5) |
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4.3 A critique of Boltzmann's approach |
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93 | (3) |
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5 Time irreversibility and the H-theorem |
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96 | (24) |
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96 | (1) |
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97 | (3) |
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5.3 Poincare's recurrence and Zermelo's paradox |
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100 | (2) |
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5.4 The physical and mathematical resolution of the paradoxes |
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102 | (7) |
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5.5 Time's arrow and the expanding universe |
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109 | (3) |
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5.6 Is irreversibility objective or subjective? |
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112 | (6) |
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118 | (2) |
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6 Boltzmann's relation and the statistical interpretation of entropy |
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120 | (14) |
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6.1 The probabilistic interpretation of thermodynamics |
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120 | (1) |
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6.2 Explicit use of probability for a gas with discrete energies |
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121 | (4) |
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125 | (4) |
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6.4 The so-called H-curve |
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129 | (5) |
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7 Boltzmann, Gibbs, and equilibrium statistical mechanics |
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134 | (19) |
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134 | (1) |
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7.2 A great American scientist of the nineteenth century: J.W. Gibbs |
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135 | (5) |
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7.3 Why is statistical mechanics usually attributed to Gibbs and not to Boltzmann? |
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140 | (2) |
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142 | (3) |
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7.5 French scientists on statistical mechanics |
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145 | (1) |
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7.6 The problem of trend to equilibrium and ergodic theory |
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146 | (4) |
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7.7 Planck and statistical mechanics |
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150 | (3) |
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8 The problem of polyatomic molecules |
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153 | (7) |
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8.1 The problem of specific heats |
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153 | (1) |
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8.2 The H-theorem for polyatomic molecules |
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154 | (1) |
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155 | (2) |
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8.4 Boltzmann's ideas on specific heats, and twentieth century contributions |
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157 | (3) |
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9 Boltzmann's contributions to other branches of physics |
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160 | (10) |
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9.1 Boltzmann's testing of Maxwell's theory of electromagnetism |
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160 | (1) |
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9.2 Boltzmann lays the foundations of hereditary mechanics |
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161 | (1) |
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9.3 Back to electromagnetism |
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162 | (1) |
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9.4 A true pearl of theoretical physics |
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163 | (1) |
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9.5 Mathematics and foundations of mechanics |
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164 | (6) |
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10 Boltzmann as a philosopher |
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170 | (28) |
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10.1 A realist, but not a naive one |
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170 | (1) |
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10.2 Laws of thought and scientific concepts |
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177 | (4) |
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10.3 Ethics, aesthetics, religion |
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181 | (3) |
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10.4 Philosophy of science |
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184 | (5) |
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10.5 Boltzmann's views on scientific revolutions |
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189 | (2) |
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10.6 Boltzmann's education in philosophy |
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191 | (1) |
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10.7 Did Boltzmann abandon realism? |
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192 | (6) |
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11 Boltzmann and his contemporaries |
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198 | (16) |
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11.1 The contacts between Boltzmann and his colleagues |
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198 | (1) |
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198 | (2) |
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200 | (2) |
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11.4 Boltzmann and the energetists |
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202 | (8) |
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210 | (1) |
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11.6 Students and younger colleagues |
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211 | (3) |
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12 The influence of Boltzmann's ideas on the science and technology of the twentieth century |
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214 | (12) |
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214 | (1) |
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215 | (2) |
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12.3 Black-body radiation |
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217 | (3) |
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220 | (3) |
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12.5 The role of Boltzmann's ideas during the twentieth century |
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223 | (3) |
Epilogue |
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226 | (1) |
Chronology |
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227 | (4) |
"A German professor's journey into Eldorado" |
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231 | (20) |
Appendices |
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251 | (46) |
A 3.1 Calculation of pressure in a rarefied gas |
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251 | (4) |
A 4.1 The Liouville equation |
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255 | (4) |
A 4.2 Calculation of the effect of collisions of one particle with another |
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259 | (2) |
A 4.3 The BBGKY hierarchy |
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261 | (3) |
A 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equation |
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264 | (2) |
A 4.5 The Boltzmann equation in the homogeneous isotropic case |
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266 | (1) |
A 5.1 Collision-invariants |
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267 | (4) |
A 5.2 Boltzmann's inequality and the Maxwell distribution |
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271 | (2) |
A 5.3 The H-theorem |
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273 | (4) |
A 5.4 The hourglass model |
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277 | (3) |
A 6.1 Likelihood of a distribution |
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280 | (3) |
A 7.1 The canonical distribution for equilibrium states |
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283 | (4) |
A 8.1 The H-theorem for classical polyatomic molecules |
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287 | (4) |
A 8.2 The equipartition problem |
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291 | (3) |
A 9.1 The Stefan-Boltzmann law |
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294 | (1) |
A 9.2 Wien's law |
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295 | (2) |
References |
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297 | (22) |
Index |
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319 | |