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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 compact summaries 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.
Chapter 1: Thermodynamics, Fundamentals
First Law of Thermodynamics
Second Law
Variational Statement of Second Law
Application: Thermal Equilibrium and Temperature
Auxiliary Functions and Legend Transforms
Maxwell Relations
Extensive Functions and the Gibbs-Duhem Equation
Intensive Functions
Chapter 2: Conditions for Equilibrium and Stability
Multiphase Equilibrium
Stability
Application to Phase Equilibria
Plane Interfaces
Chapter 3: Statistical Mechanics
The Statistical Method and Ensembles
Microcanonical Ensemble and the Rational Foundation of Thermodynamics
Canonical Ensemble
A Simple Example
Generalized Ensembles and the Gibbs Entropy Formula
Fluctuations Involving Uncorrelated Particles
Alternative Development of Equilibrium Distribution Functions
Chapter 4: Non-Interacting (Ideal) Systems
Occupation Numbers
Photon Gas
Phonon Gas
Ideal Gases of Real Particles
Electrons in Metals
Classical Ideal Gases, the Classical Limit
Thermodynamics of an Ideal Gas of Structureless Classical Particles
A Dilute Gas of Atoms
A Dilute Gas of Diatomic Molecules
Chemical Equilibria in Gases
Chapter 5: Statistical Mechanical Theory of Phase Transitions
Ising Model
Lattice Gas
Broken Symmetry and Range of Correlations
Mean Field Theory
Variational Treatment of Mean Field Theory
Renormalization Group (RG) Theory
RG Theory for the Two Dimensional Ising Model
Isomorphism Between Two-Level Quantum Mechanical System and the Ising Model
Chapter 6: Monte Carlo Method in Statistical Mechanics
Trajectories
A Monte Carlo Trajectory
Non-Boltzmann Sampling
Quantum Monte Carlo
Chapter 7: Classical Fluids
Averages in Phase Space
Reduced Configurational Distribution Functions
Reversible Work Theorem
Thermodynamic Properties from g(r)
Measurement of g(r) by Diffraction
Solvation and Chemical Equilibrium in Liquids
Molecular Liquids
Monte Carlo for Hard Disks
Chapter 8: Statistical Mechanics of Non-Equilibrium Systems
Systems Close to Equilibrium
Onsager's Regression Hypothesis and Time Correlation Functions
Application: Chemical Kinetics
Another Application: Self Diffusion
Fluctuation Dissipation Theorem
Response Functions
Absorption
Friction and the Langevin Equation
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 compact summaries 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
Chapter 1: Thermodynamics, Fundamentals
First Law of Thermodynamics
Second Law
Variational Statement of Second Law
Application: Thermal Equilibrium and Temperature
Auxiliary Functions and Legend Transforms
Maxwell Relations
Extensive Functions and the Gibbs-Duhem Equation
Intensive Functions
Chapter 2: Conditions for Equilibrium and Stability
Multiphase Equilibrium
Stability
Application to Phase Equilibria
Plane Interfaces
Chapter 3: Statistical Mechanics
The Statistical Method and Ensembles
Microcanonical Ensemble and the Rational Foundation of Thermodynamics
Canonical Ensemble
A Simple Example
Generalized Ensembles and the Gibbs Entropy Formula
Fluctuations Involving Uncorrelated Particles
Alternative Development of Equilibrium Distribution Functions
Chapter 4: Non-Interacting (Ideal) Systems
Occupation Numbers
Photon Gas
Phonon Gas
Ideal Gases of Real Particles
Electrons in Metals
Classical Ideal Gases, the Classical Limit
Thermodynamics of an Ideal Gas of Structureless Classical Particles
A Dilute Gas of Atoms
A Dilute Gas of Diatomic Molecules
Chemical Equilibria in Gases
Chapter 5: Statistical Mechanical Theory of Phase Transitions
Ising Model
Lattice Gas
Broken Symmetry and Range of Correlations
Mean Field Theory
Variational Treatment of Mean Field Theory
Renormalization Group (RG) Theory
RG Theory for the Two Dimensional Ising Model
Isomorphism Between Two-Level Quantum Mechanical System and the Ising Model
Chapter 6: Monte Carlo Method in Statistical Mechanics
Trajectories
A Monte Carlo Trajectory
Non-Boltzmann Sampling
Quantum Monte Carlo
Chapter 7: Classical Fluids
Averages in Phase Space
Reduced Configurational Distribution Functions
Reversible Work Theorem
Thermodynamic Properties from g(r)
Measurement of g(r) by Diffraction
Solvation and Chemical Equilibrium in Liquids
Molecular Liquids
Monte Carlo for Hard Disks
Chapter 8: Statistical Mechanics of Non-Equilibrium Systems
Systems Close to Equilibrium
Onsager's Regression Hypothesis and Time Correlation Functions
Application: Chemical Kinetics
Another Application: Self Diffusion
Fluctuation Dissipation Theorem
Response Functions
Absorption
Friction and the Langevin Equation