Statistical Mechanics

by Dorlas, Teunis C.

• ISBN13: 9780750305402
• ISBN10: 0750305401
• Format: Paperback
• Copyright: 1999-11-01
• Publisher: Inst of Physics Pub Inc

Summary

Presents an introduction to thermodynamics and statistical mechanics from a mathematical point of view. Suitable for advanced undergraduate or beginning postgraduate students of mathematics and physics with a knowledge or probability theory, real analysis and the rudiments of Newtonian mechanics. Softcover.

Table of Contents

Preface	ix
Introduction	xi
Acknowledgments	xix
PART I: Thermodynamics	1	(90)
The Zeroth Law	3	(3)
The First Law	6	(6)
Differentials	12	(4)
The Second Law	16	(6)
Thermal Engines and Refrigerators	22	(5)
The Fundamental Equation	27	(6)
Convexity	33	(7)
Thermodynamic Potentials	40	(4)
Phase Transitions	44	(7)
Magnetism	51	(4)
The Refrigerator and Liquefaction of Gases	55	(8)
Examples of Phase Transitions	63	(6)
Equations of state for Solids	69	(2)
Applications in Chemistry	71	(2)
Black-Body Radiation	73	(3)
The Big Bang	76	(4)
The Constitution of Stars	80	(4)
Problems to Part I	84	(7)
PART II: Fundamentals of Statistical Mechanics	91	(64)
Quantum Mechanics	93	(11)
Non-Interacting Localized Spins	104	(5)
Large-Deviation Theory	109	(11)
The Paramagnet Revisited	120	(4)
Identical Localized Free Particles	124	(4)
Quantum Gases	128	(7)
Ensembles	135	(4)
Existence of the Thermodynamic Limit	139	(5)
Large Deviations for the Energy Density	144	(4)
Problems to Part II	148	(7)
PART III: Models in Statistical Mechanics	155	(76)
A Simple Model for Rubber	157	(3)
The Ising Model	160	(14)
The Mean-Field Weiss--Ising Model	174	(5)
The Mean-Field Lattice Gas	179	(6)
Metals and the Electron Gas	185	(5)
White-Dwarf Stars	190	(6)
Phonons	196	(4)
Boson Condensation and Liquid Helium	200	(10)
Superconductivity	210	(14)
Problems to Part III	224	(7)
Appendices
Probability Theory	231	(8)
Quantum Mechanics	239	(10)
Convexity	249	(7)
References	256	(2)
Further Reading	258	(3)
Answers to the Problems	261	(6)
Index	267