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720 Pages
23.5 x 15.88 x 3.18
Hardcover
$329.00
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Industry Reviews
From the reviews of the first edition:
"Gibbs introduced one century ago an axiomatic approach to statistical mechanics. The a posteriori remarkable success of the Gibbsian formalism is, however, even today in sharp contrast to our lack of understanding of its mechanical foundation. The book The Logic of Thermostatiscal Physics puts into perspective this contrast for classical mechanical systems and for their quantum mechanical counterparts. [...] The book deals with many aspects of not only the logical but also the physical foundation of thermostatistics. Tracing the history of its development makes it a pleasure to read." (Mathematical Reviews 2003g)
"[This] clearly written book contains interesting historical remarks and shows the philosophy behind thermo-statistics. The extraordinarily detailed list of references and its far-reaching range makes the book valuable for mathematicians, physicists and philosophers of science in research and teaching. Its representation may stimulate further philosophical investigations." (Zentralblatt MATH 2004, vol. 1033, page 571)
"This book is a tremendously erudite and comprehensive resource in foundations of statistical mechanics. It is also a significant contribution to the philosophical discussion of models and theories. Philosophers will value the applications of the semantic view of the theories to a wide range of cases in physics. ... For those doing research in foundations of statistical physics, having this wealth of information in one place will prove invaluable." (Craig Callender, Studies in History and Philosophy of Modern Physics, Vol. 35, 2004)
"In this book a mathematical physicist and a philosopher report on their professional struggle with the foundational problems of thermodynamics and statistical mechanics. ... It is an excellent historical and technical introduction to the BCS theory of superconductivity, and to more recent work on mean field models of dilute gas BEC." (C. Savage, The Physicist, Vol. 39 (3), 2002)
| Theories and Models: a Philosophical Overview | p. 1 |
| Introduction | p. 1 |
| The Syntactic vs. the Semantic View | p. 2 |
| Conceptions of Models | p. 11 |
| Models and Semantics: a Hybrid View | p. 16 |
| Semantic View and Theory Testing (Confirmation) | p. 22 |
| Semantic View and Theory Reduction | p. 26 |
| Semantic View and Structural Explanation | p. 34 |
| Thermostatics | p. 39 |
| Introduction | p. 39 |
| Thermometry | p. 41 |
| TheMotive Power of Heat vs. Conservation Laws | p. 47 |
| Energy vs. Entropy | p. 63 |
| The Syntax of Thermodynamics | p. 65 |
| TheSemantics of Thermodynamics | p. 66 |
| Kinetic Theory of Gases | p. 81 |
| A Random Walk Model for Diffusion | p. 81 |
| The Maxwell Distribution | p. 87 |
| The Boltzmann Equation | p. 92 |
| TheDog-FleaModel | p. 106 |
| Classical Probability | p. 113 |
| Different Models for Probability | p. 113 |
| From Gamblers to Statisticians | p. 115 |
| From Combinatorics to Analysis | p. 127 |
| From Here to Where? | p. 144 |
| Modern Probability: Syntax and Models | p. 153 |
| QuietandQuaintNoMore | p. 153 |
| From Hilbert's 6th Problem to Kolmogorov's Syntax | p. 156 |
| Shannon's Entropy | p. 175 |
| The Transcendence of Randomness | p. 188 |
| Modern Probability: Competing Semantics | p. 199 |
| VonMises' Semantics | p. 199 |
| Algorithmic Complexity and Randomness | p. 205 |
| DeFinetti's Semantics | p. 215 |
| Setting-up the Ergodic Problem | p. 237 |
| Boltzmann's Heuristics | p. 237 |
| Formal Responses: Birkhoff/von Neumann | p. 250 |
| Models and Ergodic Hierarchy | p. 261 |
| Mixing Properties | p. 262 |
| K-Systems | p. 268 |
| Dynamical Entropy | p. 278 |
| Anosov Property | p. 284 |
| Ergodicity vs. Integrability | p. 295 |
| Is Ergodicity Generic? | p. 295 |
| Integrable Systems | p. 301 |
| A Tale of Two Models: Approximation or Error? | p. 304 |
| The KAM Tori | p. 310 |
| Conclusions and Remaining Issues | p. 317 |
| The Gibbs Canonical Ensembles | p. 331 |
| Classical Settings | p. 331 |
| Quantum Extensions | p. 346 |
| Traditional Formalism | p. 346 |
| The KMS Condition | p. 349 |
| Early Successes | p. 357 |
| Phase Transitions: van der Waals to Lenz | p. 373 |
| Introduction | p. 373 |
| Thermodynamical Models | p. 375 |
| Mean-Field Models | p. 380 |
| The van der Waals Model of Fluids | p. 380 |
| The van der Waals Equation from Statistical Mechanics | p. 386 |
| The Weiss Model for Ferromagnets | p. 389 |
| Ising and Related Models | p. 393 |
| The 1-d Ising Model. No-Go Theorems | p. 393 |
| The 2-d IsingModel | p. 403 |
| Variations on the Theme of the Ising Model | p. 419 |
| Variations on the Interpretation of the Variables | p. 419 |
| Variations Involving the Range of the Variables | p. 421 |
| Variations Modifying the Domain or Range of the Interactions | p. 425 |
| Scaling and Renormalization | p. 431 |
| Scaling Hypotheses and Scaling Laws | p. 431 |
| The Renormalization Program | p. 435 |
| Quantum Models for Phase Transitions | p. 451 |
| Superconductivity and the BCS Model | p. 451 |
| Preliminaries to the BCS Model | p. 451 |
| The Essentials of the BCS Model | p. 457 |
| Superconductivity after BCS | p. 461 |
| Superfluidity and Bose-Einstein Condensation | p. 462 |
| TheEarlyDays | p. 462 |
| Modern Developments | p. 467 |
| Approach to Equilibrium in Quantum Mechanics | p. 477 |
| Introduction | p. 477 |
| Master Equations | p. 479 |
| Approach to Equilibrium: Quantum Models | p. 495 |
| The Philosophical Horizon | p. 519 |
| General Issues | p. 519 |
| Model-Building: Idealization and Approximation | p. 521 |
| Model-Building: Simulation | p. 526 |
| Recapitulation | p. 532 |
| Models in Mathematical Logic | p. 539 |
| Syntax | p. 539 |
| Semantics | p. 544 |
| The Calculus of Differentials | p. 553 |
| Green's Theorem | p. 553 |
| Stokes' and Gauss' Theorems | p. 559 |
| Higher Differentials | p. 565 |
| Recursive Functions | p. 575 |
| Topological Essences | p. 585 |
| Basic Definitions | p. 585 |
| ExamplesfromFunctional Analysis | p. 590 |
| Separability and Compactness | p. 600 |
| The Baire Essentials | p. 605 |
| Models vs. Models | p. 607 |
| Models in Wigner's Writings and in the Third Wigner Symposium | p. 607 |
| A Search for Precedents | p. 608 |
| The Case | p. 611 |
| Closing Statements | p. 613 |
| References | p. 617 |
| Citation Index | p. 677 |
| Subject Index | p. 693 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9783540413790
ISBN-10: 3540413790
Published: 30th November 2001
Format: Hardcover
Language: English
Number of Pages: 720
Audience: General Adult
Publisher: Springer Nature B.V.
Country of Publication: DE
Dimensions (cm): 23.5 x 15.88 x 3.18
Weight (kg): 1.11
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