Verfügbarkeit: The logic of thermostatistical physics

The logic of thermostatistical physics:

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Emch, Gérard G. 1936- (VerfasserIn), Liu, Chuang 1958- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2002
Schriftenreihe:	Physics and astronomy online library
Schlagworte:	Mathematische Logik Statistische Thermodynamik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 703 S.
ISBN:	3540413790

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS 1. THEORIES AND MODELS: A PHILOSOPHICAL OVERVIEW ........... 1 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 THE SYNTACTIC VS. THE SEMANTIC VIEW . . . . . . . . . . . . . . . . . . . . . . 2 1.3 CONCEPTIONS OF MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 MODELS AND SEMANTICS: A H YBRID VIEW . . . . . . . . . . . . . . . . . . . . 16 1.5 SEMANTIC VIEW AND THEORY TESTING (CONFIRMATION) . . . . . . . . . 22 1.6 SEMANTIC VIEW AND THEORY REDUCTION . . . . . . . . . . . . . . . . . . . . . 26 1.7 SEMANTIC VIEW AND STRUCTURAL EXPLANATION . . . . . . . . . . . . . . . . 34 2. THERMOSTATICS ............................................ 39 2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2 THERMOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3 THE MOTIVE POWER OF H EAT VS. CONSERVATION LAWS. . . . . . . . . . . 47 2.4 ENERGY VS. ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.4.1 THE SYNTAX OF THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . 65 2.4.2 THE SEMANTICS OF THERMODYNAMICS . . . . . . . . . . . . . . . . . 66 3. KINETIC THEORY OF GASES .................................. 81 3.1 A RANDOM WALK MODEL FOR DIFFUSION . . . . . . . . . . . . . . . . . . . . . . 81 3.2 THE MAXWELL DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 THE BOLTZMANN EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.4 THE DOG-FLEA MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4. CLASSICAL PROBABILITY ...................................... 113 4.1 DIFFERENT MODELS FOR PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.2 FROM GAMBLERS TO STATISTICIANS . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.3 FROM COMBINATORICS TO ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.4 FROM H ERE TO WHERE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5. MODERN PROBABILITY: SYNTAX AND MODELS . . . . . . . . . . . . . . . . . . 153 5.1 QUIET AND QUAINT NO MORE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 FROM HILBERTS 6TH PROBLEM TO KOLMOGOROVS SYNTAX . . . . . . . . 156 5.3 SHANNONS ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.4 THE TRANSCENDENCE OF RANDOMNESS . . . . . . . . . . . . . . . . . . . . . . . 188 XII CONTENTS 6. MODERN PROBABILITY: COMPETING SEMANTICS ............... 199 6.1 VON MISES SEMANTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.2 ALGORITHMIC COMPLEXITY AND RANDOMNESS . . . . . . . . . . . . . . . . . 205 6.3 DE FINETTIS SEMANTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7. SETTING-UP THE ERGODIC PROBLEM .......................... 237 7.1 BOLTZMANNS H EURISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 7.2 FORMAL RESPONSES: BIRKHOFF/VON NEUMANN . . . . . . . . . . . . . . . . . 250 8. MODELS AND ERGODIC HIERARCHY ............................ 261 8.1 MIXING PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 8.2 K-SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 8.3 DYNAMICAL ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 8.4 ANOSOV PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 9. ERGODICITY VS. INTEGRABILITY ............................... 295 9.1 IS ERGODICITY GENERIC? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 9.2 INTEGRABLE SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 9.3 A TALE OF TWO MODELS: APPROXIMATION OR ERROR? . . . . . . . . . . . 304 9.4 THE KAM TORI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 9.5 CONCLUSIONS AND REMAINING ISSUES . . . . . . . . . . . . . . . . . . . . . . . . 317 10. THE GIBBS CANONICAL ENSEMBLES .......................... 331 10.1 CLASSICAL SETTINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 10.2 QUANTUM EXTENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 10.2.1 TRADITIONAL FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 10.2.2 THE KMS CONDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 10.3 EARLY SUCCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 11. PHASE TRANSITIONS: VAN DER WAALS TO LENZ ................. 373 11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 11.2 THERMODYNAMICAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 11.3 MEAN-FIELD MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 11.3.1 THE VAN DER WAALS MODEL OF FLUIDS . . . . . . . . . . . . . . . . . 380 11.3.2 THE VAN DER WAALS EQUATION FROM STATISTICAL MECHANICS 386 11.3.3 THE WEISS MODEL FOR FERROMAGNETS . . . . . . . . . . . . . . . . . 389 12. ISING AND RELATED MODELS ................................. 393 12.1 THE 1-D ISING MODEL. NO-GO THEOREMS . . . . . . . . . . . . . . . . . . . . 393 12.2 THE 2-D ISING MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 12.3 VARIATIONS ON THE THEME OF THE ISING MODEL. . . . . . . . . . . . . . . . 419 12.3.1 VARIATIONS ON THE INTERPRETATION OF THE VARIABLES . . . . . 419 12.3.2 VARIATIONS INVOLVING THE RANGE OF THE VARIABLES . . . . . . 421 12.3.3 VARIATIONS MODIFYING THE DOMAIN OR RANGE OF THE INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 CONTENTS XIII 13. SCALING AND RENORMALIZATION .............................. 431 13.1 SCALING H YPOTHESES AND SCALING LAWS . . . . . . . . . . . . . . . . . . . . . 431 13.2 THE RENORMALIZATION PROGRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 14. QUANTUM MODELS FOR PHASE TRANSITIONS ................... 451 14.1 SUPERCONDUCTIVITY AND THE BCS MODEL . . . . . . . . . . . . . . . . . . . . 451 14.1.1 PRELIMINARIES TO THE BCS MODEL . . . . . . . . . . . . . . . . . . . . 451 14.1.2 THE ESSENTIALS OF THE BCS MODEL . . . . . . . . . . . . . . . . . . . 457 14.1.3 SUPERCONDUCTIVITY AFTER BCS . . . . . . . . . . . . . . . . . . . . . . . 461 14.2 SUPERFLUIDITY AND BOSEEINSTEIN CONDENSATION . . . . . . . . . . . . . 462 14.2.1 THE EARLY DAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 14.2.2 MODERN DEVELOPMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 15. APPROACH TO EQUILIBRIUM IN QUANTUM MECHANICS ......... 477 15.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 15.2 MASTER EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 15.3 APPROACH TO EQUILIBRIUM: QUANTUM MODELS . . . . . . . . . . . . . . . . 495 16. THE PHILOSOPHICAL HORIZON ................................ 519 16.1 GENERAL ISSUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 16.2 MODEL-BUILDING: IDEALIZATION AND APPROXIMATION . . . . . . . . . . . 521 16.3 MODEL-BUILDING: SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 16.4 RECAPITULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 A. APPENDIX: MODELS IN MATHEMATICAL LOGIC ................. 539 A.1 SYNTAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 A.2 SEMANTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 B. APPENDIX: THE CALCULUS OF DIFFERENTIALS .................. 553 B.1 GREENS THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 B.2 STOKES* AND GAUSS* THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 B.3 H IGHER DIFFERENTIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 C. APPENDIX: RECURSIVE FUNCTIONS ........................... 575 D. APPENDIX: TOPOLOGICAL ESSENCES .......................... 585 D.1 BASIC DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 D.2 EXAMPLES FROM FUNCTIONAL ANALYSIS. . . . . . . . . . . . . . . . . . . . . . . 590 D.3 SEPARABILITY AND COMPACTNESS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 D.4 THE BAIRE ESSENTIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 E. APPENDIX: MODELS VS. MODELS ............................ 607 E.1 MODELS IN WIGNER*S WRITINGS AND IN THE THIRD WIGNER SYMPOSIUM . . . . . . . . . . . . . . . . . . . . . 607 E.2 A SEARCH FOR PRECEDENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 XIV CONTENTS E.3 THE CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 E.4 CLOSING STATEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613 REFERENCES .................................................... 617 CITATION INDEX ................................................ 677 SUBJECT INDEX ................................................ 693
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spelling	Emch, Gérard G. 1936- Verfasser (DE-588)12327415X aut The logic of thermostatistical physics Gérard G. Emch ; Chuang Liu Berlin [u.a.] Springer 2002 XIV, 703 S. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 s Mathematische Logik (DE-588)4037951-6 s DE-604 Liu, Chuang 1958- Verfasser (DE-588)123274214 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009612503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Emch, Gérard G. 1936- Liu, Chuang 1958- The logic of thermostatistical physics Mathematische Logik (DE-588)4037951-6 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd
subject_GND	(DE-588)4037951-6 (DE-588)4126251-7
title	The logic of thermostatistical physics
title_auth	The logic of thermostatistical physics
title_exact_search	The logic of thermostatistical physics
title_full	The logic of thermostatistical physics Gérard G. Emch ; Chuang Liu
title_fullStr	The logic of thermostatistical physics Gérard G. Emch ; Chuang Liu
title_full_unstemmed	The logic of thermostatistical physics Gérard G. Emch ; Chuang Liu
title_short	The logic of thermostatistical physics
title_sort	the logic of thermostatistical physics
topic	Mathematische Logik (DE-588)4037951-6 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd
topic_facet	Mathematische Logik Statistische Thermodynamik
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