Mathematical Foundations of Statistical Mechanics (eBook)

A. Ya. Khinchin (Autor)

eBook Download: EPUB

2013
179 Seiten
Dover Publications (Verlag)
978-0-486-13873-2 (ISBN)

Infos

Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Reduction to the Problem of the Theory of Probability; and more.

Inhalt

PrefaceChapter I. Introduction1. A brief historical sketch2. Methodological characterizationChapter II. Geometry and Kinematics of the Phase Space3. The phase space of a mechanical system4. Theorem of Liouville5. Theorem of Birkhoff6. Case of metric indecomposability7. Structure functions8. Components of mechanical systemsChapter III. Ergodic Problem9. Interpretation of physical quantities in statistical mechanics10. Fixed and free integrals11. Brief historical sketch12. On metric indecomposability of reduced manifolds13. The possibility of a formulation without the use of metric indecomposabilityChapter IV. Reduction to the Problem of the Theory of Probability14. Fundamental distribution law15. The distribution law of a component and its energy16. Generating functions 17. Conjugate distribute functions18. Systems consisting of a large number of componentsChapter V. Application of the Central Limit Theorem19. Approximate expressions of structure functions20. The small component and its energy. Boltzmann's law21. Mean values of the sum functions22. Energy distribution law of the large component23. Example of monatomic ideal gas24. The theorem of equipartition of energy25. A system in thermal equilibrium. Canonical distribution of GibbsChapter VI. Ideal Monatomic Gas26. Velocity distribution. Maxwell's law27. The gas pressure28. Physical interpretation of the parameter29. Gas pressure in an arbitrary field of forceChapter VII. The Foundation of Thermodynamics30. External parameters and the mean values of external forces31. The volume of the gas as an external parameter32. The second law of thermodynamics33. The properties of entropy34. Other thermodynamical functionsChapter VIII. Dispersion and the Distributions of Sum Functions35. The intermolecular correlation36. Dispersion and distribution laws of the sum functionsAppendix The proof of the central limit theorem of the theory of probabilityNotationsIndex

Produkt-Details

• Erscheint lt. Verlag: 17.1.2013
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 249 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 0-486-13873-9 / 0486138739
• ISBN-13: 978-0-486-13873-2 / 9780486138732