Introduction to Modern Statistical Mechanics

by Chandler, David

• ISBN13: 9780195042771
• ISBN10: 0195042778
• Format: Paperback
• Copyright: 1987-09-17
• Publisher: Oxford University Press

Summary

Leading physical chemist David Chandler takes a new approach to statistical mechanics to provide the only introductory-level work on the modern topics of renormalization group theory, Monte Carlo simulations, time correlation functions, and liquid structure. The author provides compactsummaries of the fundamentals of this branch of physics and discussions of many of its traditional elementary applications, interspersed with over 150 exercises and microcomputer programs.

Table of Contents

Thermodynamics, Fundamentals	3	(28)
First Law of Thermodynamics and Equilibrium	4	(4)
Second Law	8	(3)
Variational Statement of Second Law	11	(2)
Application: Thermal Equilibrium and Temperature	13	(3)
Auxiliary Functions and Legendre Transforms	16	(4)
Maxwell Relations	20	(2)
Extensive Functions and the Gibbs-Duhem Equation	22	(2)
Intensive Functions	24	(4)
Additional Exercises	25	(2)
Bibliography	27	(1)
Conditions for Equilibrium and Stability	28	(26)
Multiphase Equilibrium	29	(4)
Stability	33	(4)
Application to Phase Equilibria	37	(7)
Plane Interfaces	44	(10)
Additional Exercises	49	(3)
Bibliography	52	(2)
Statistical Mechanics	54	(32)
The Statistical Method and Ensembles	55	(4)
Microcanonical Ensemble and the Rational Foundation of Thermodynamics	59	(3)
Canonical Ensemble	62	(4)
A Simple Example	66	(3)
Generalized Ensembles and the Gibbs Entropy Formula	69	(3)
Fluctuations Involving Uncorrelated Particles	72	(2)
Alternative Development of Equilibrium Distribution Functions	74	(12)
Additional Exercises	79	(5)
Bibliography	84	(2)
Non-Interacting (Ideal) Systems	86	(33)
Occupation Numbers	89	(1)
Photon Gas	90	(2)
Phonon Gas or Fluctuations of Atomic Positions in a Cold Solid	92	(2)
Ideal Gases of Real Particles	94	(3)
Electrons in Metals	97	(3)
Classical Ideal Gases, the Classical Limit	100	(3)
Thermodynamics of an Ideal Gas of Structureless Classical Particles	103	(2)
A Dilute Gas of Atoms	105	(1)
Dilute Gas of Diatomic Molecules	106	(5)
Chemical Equilibria in Gases	111	(8)
Additional Exercises	113	(5)
Bibliography	118	(1)
Satistical Mechanical Theory of Phase Transitions	119	(40)
Ising Model	119	(5)
Lattice Gas	124	(1)
Broken Symmetry and Range of Correlations	125	(6)
Mean Field Theory	131	(4)
Variational Treatiment of Mean Field Theory	135	(4)
Renormalization Group (RG) Theory	139	(4)
RG Theory for the Two-Dimensional Ising Model	143	(6)
Isomorphism between Two-Level Quantum Mechanical System and the Ising Model	149	(10)
Additional Exercises	154	(4)
Bibliography	158	(1)
Monte Carlo Method in Satistical Mechanics	159	(29)
Trajectories	160	(3)
A Monte Carlo Trajectory	163	(5)
Non-Boltzmann Sampling	168	(7)
Quantum Monte Carlo	175	(13)
Additional Exercises	178	(4)
Bibliography	182	(2)
Appendix	184	(4)
Classical Fluids	188	(46)
Averages in Phase Space	189	(6)
Reduced Configurational Distribution Functions	195	(6)
Reversible Work Theorem	201	(1)
Thermodynamic Properties from g (r)	202	(5)
Measurement of g (r) by Diffraction	207	(2)
Solvation and Chemical Equilibrium in Liquids	209	(4)
Molecular Liquids	213	(5)
Monte Carlo for Hard Disks	218	(16)
Additional Exercises	223	(5)
Bibliography	228	(2)
Appendix	230	(4)
Statistical Mechanics of Non-Equilibrium Systems	234	(37)
Systems Close to Equilibrium	235	(2)
Onsager's Regression Hypothesis and Time Correlation Functions	237	(5)
Application: Chemical Kinetics	242	(4)
Another Application: Self-Diffusion	246	(6)
Fluctuation-Dissipation Theorem	252	(3)
Response Functions	255	(3)
Absorption	258	(3)
Friction and the Langevin Equation	261	(10)
Additional Exercises	266	(4)
Bibliography	270	(1)
Index	271