A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.
Review of theoretical definitions and formulae
Notation used throughout the book
Thermodynamics
First and second law
Thermodynamic potentials and quantities
Maxwell relations
Simple thermodynamic processes
Statistical Ensembles
Microcanonical, canonical, and grand canonical ensembles
Connection with thermodynamics
Equipartition theorem
Noninteracting gases of classical particles
Noninteracting lattice-type systems
Gases of molecules
Quantum Statistics
Statistics of indistinguishable particles, bosons, and fermions
Density of states
Black body radiation
Debye's models for solids
Bose condensation
Fermi gas
Interacting Systems
Classical gases and virial coefficients
Critical exponents in phase transitions
Ising type models and Heisenberg modes
Exact and mean field approaches
Nonequilibrium Systems
Random walk
Markov chains
Master equation
Diffusion phenomena
Boltzmann transport equation
Relaxation time approximation
Appendix: Useful Mathematical Formulae
Index
"The best way to learn a skill is by active practice. This wonderful collection of statistical mechanics problems, compiled by the trio, supplies a host of interesting questions and carefully worked-out solutions. Anyone with a basic background in statistical mechanics and thermodynamics can pick up the book and start practice sessions."
- Henrik Jeldtoft Jensen, Mathematics, Physics and Engineering
