The Logic of Thermostatistical Physics

Pirmais vāks
Springer Science & Business Media, 2002 - 703 lappuses
This 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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Atlasītās lappuses

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
Subject Index
691
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