The Logic of Thermostatistical PhysicsThis book addresses several of the foundational problems in thermophysics, i. e. thermodynamics and statistical mechanics. It is an interdisciplinary work in that it examines the philosophical underpinning of scientific models and theories; it also refines the analysis of the problems at hand and delineates the place occupied by various scientific models in a generalized philosophical landscape. Hence, our philosophical - or theoretical - inquiry focuses sharply on the concept of models; and our empirical - or laboratory - evidence is sought in the model-building activities of scientists who have tried to confront the epistemological problems arising in the thermophysical sciences. Primarily for researchers and students in physics, philosophy of science, and mathematics, our book aims at informing the readers - with all the in dispensable technical details made readily available - about the nature of the foundational problems, how these problems are approached with the help of various mathematical models, and what the philosophical implications of such models and approaches involve. Some familiarity with elementary ther mophysics and/or with introductory-level philosophy of science may help, but neither is a prerequisite. The logical and mathematical background re quired for the book are introduced in the Appendices. Upon using the Subject Index, the readers may easily locate the concepts and theorems needed for understanding various parts of the book. The Citation Index lists the authors of the contributions we discuss in detail. |
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Saturs
a Philosophical Overview | 1 |
12 The Syntactic vs the Semantic View | 2 |
13 Conceptions of Models | 11 |
a Hybrid View | 16 |
15 Semantic View and Theory Testing Confirmation | 22 |
16 Semantic View and Theory Reduction | 26 |
17 Semantic View and Structural Explanation | 34 |
2 Thermostatics | 39 |
103 Early Successes | 357 |
van der Waals to Lenz | 373 |
112 Thermodynamical Models | 375 |
113 MeanField Models | 380 |
1132 The van der Waals Equation from Statistical Mechanics | 386 |
1133 The Weiss Model for Ferromagnets | 389 |
12 Ising and Related Models | 393 |
122 The 2d Ising Model | 403 |
22 Thermometry | 41 |
23 The Motive Power of Heat vs Conservation Laws | 47 |
24 Energy vs Entropy | 63 |
241 The Syntax of Thermodynamics | 65 |
242 The Semantics of Thermodynamics | 66 |
3 Kinetic Theory of Gases | 81 |
32 The Maxwell Distribution | 87 |
33 The Boltzmann Equation | 92 |
34 The DogFlea Model | 106 |
4 Classical Probability | 113 |
42 From Gamblers to Statisticians | 115 |
43 From Combinatorics to Analysis | 127 |
44 From Here to Where? | 144 |
Syntax and Models | 153 |
52 From Hilberts 6th Problem to Kolmogorovs Syntax | 156 |
53 Shannons Entropy | 175 |
54 The Transcendence of Randomness | 188 |
Competing Semantics | 199 |
62 Algorithmic Complexity and Randomness | 205 |
63 De Finettis Semantics | 215 |
7 Settingup the Ergodic Problem | 237 |
Birkhoffvon Neumann | 250 |
8 Models and Ergodic Hierarchy | 261 |
81 Mixing Properties | 262 |
82 KSystems | 268 |
83 Dynamical Entropy | 278 |
84 Anosov Property | 284 |
9 Ergodicity vs Integrability | 295 |
92 Integrable Systems | 301 |
Approximation or Error? | 304 |
94 The KAM Tori | 310 |
95 Conclusions and Remaining Issues | 317 |
10 The Gibbs Canonical Ensembles | 331 |
102 Quantum Extensions | 346 |
1022 The KMS Condition | 349 |
123 Variations on the Theme of the Ising Model | 419 |
1232 Variations Involving the Range of the Variables | 421 |
1233 Variations Modifying the Domain or Range of the Interactions | 425 |
13 Scaling and Renormalization | 431 |
132 The Renormalization Program | 435 |
14 Quantum Models for Phase Transitions | 451 |
1412 The Essentials of the BCS Model | 457 |
1413 Superconductivity after BCS | 461 |
142 Superfluidity and BoseEinstein Condensation | 462 |
1422 Modern Developments | 467 |
15 Approach to Equilibrium in Quantum Mechanics | 477 |
152 Master Equations | 479 |
Quantum Models | 495 |
16 The Philosophical Horizon | 519 |
Idealization and Approximation | 521 |
Simulation | 526 |
164 Recapitulation | 532 |
Models in Mathematical Logic | 539 |
A2 Semantics | 544 |
The Calculus of Differentials | 553 |
B2 Stokes and Gauss Theorems | 559 |
B3 Higher Differentials | 565 |
Recursive Functions | 575 |
Topological Essences | 585 |
D2 Examples from Functional Analysis | 590 |
D3 Separability and Compactness | 600 |
D4 The Baire Essentials | 605 |
Models vs Models | 607 |
E2 A Search for Precedents | 608 |
E3 The Case | 611 |
E4 Closing Statements | 613 |
References | 617 |
Citation Index | 675 |
691 | |
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