Physics 603: Methods of Statistical Physics

James J. Kelly

Spring 2002

Course: Methods of Statistical Physics -- develops the basic principles of equilibrium statistical mechanics and their application to the thermodynamics of a wide variety of physical systems.

Prerequisites: Phys 404 or equivalent. A reasonable mastery of basic thermodynamics and quantum mechanics is assumed.

Instructor: James J. Kelly         Phone: 405-6110         e-mail:

Lectures: TuTh 9:30 - 10:50         Room 4208

Office hours: W 10-12                 Room 2215 C

Although I prefer that you use the scheduled office hours, I am often available at other times also. Please come frequently.

Grader: Prof. H.H. Chen            Phone: 5-6088         e-mail:

Office hours:  F 9:00-12:00          Room 3102

Required text: Statistical Mechanics, by R.K. Pathria (Butterworth-Heinemann, 1966)

Useful supplements:

Homework: will be assigned at 1-2 week intervals and collected in class.  Assignments, due dates, and solutions will be posted at homework.  Homework is perhaps the most important component of the course and we strongly urge you to complete it as close to the due date as possible; it will be difficult to master the subject without keeping up with the homework.  Late homework must be submitted directly to the grader's campus mailbox and will be accepted, with a penalty of 25%, until grading of the current assignment has been completed.  Collaboration on homework is permitted and use of Mathematica is encouraged.

Mathematica: a powerful symbolic manipulator which provides very useful tools for the solving problems and exploring the results. Its symbolic and graphical tools allow the student to focus more upon physics than upon algebra and its numerical tools allow interesting problems which cannot be reduced to simple closed forms to be investigated without developing customized computer programs. Mathematica notebooks have been prepared for several important topics and you are encouraged to use these notebooks as templates for the solution of other problems. Several lectures will also be presented using Mathematica. The notebooks will be placed on World Wide Web servers as they become available, and may be obtained from notebooks.  An extensive collection of Mathematica tutorials is also available.

Exams: there will be two exams given during class periods (75 minutes) and a two-hour comprehensive final exam. The date and time of the final exam will be announced when available. Make-up exams will be given only when pre-arranged with the instructor or for unavoidable absences, such as documented illnesses or emergencies.

Grading: graded work will be weighted 20% for each in-class exam (40% total), 30% for homework, and 30% for the final exam. Letter grades are based upon the distribution of numerical scores.

Goals: to acquire a sound understanding of the basic principles of statistical mechanics and its application to realistic problems. Among the skills we seek to develop are:


  1. Review of thermodynamics
    1. Macroscopic description of equilibrium states
    2. Laws of thermodynamics
    3. Thermodynamic potentials and relationships
    4. Equilibrium and stability conditions
    5. Phase transitions
  2. Basic principles
    1. Density matrix formalism
    2. Statistical postulates
    3. Disorder and entropy
    4. Multiplicity functions
    5. Thermal interaction
    6. Temperature
    7. Statistical interpretation of thermodynamics
  3. Microcanonical ensemble
    1. Enumeration of microstates
    2. Large numbers
    3. Binary systems
    4. Noninteracting oscillators
  4. Canonical ensemble
    1. Definition and properties
    2. Thermodynamics
    3. Factorizable systems
      1. Paramagnetism
      2. Lattice vibrations
      3. Blackbody radiation
    4. Mean-field model of spontaneous magnetization
    5. Fluctuations and correlations
  5. Grand canonical ensemble
    1. Definition and properties
    2. Thermodynamics
    3. Occupation representation
      1. Classical
      2. Bose-Einstein
      3. Fermi-Dirac
  6. Semiclassical systems
    1. Classical phase space
    2. Entropy
    3. Maxwell-Boltzmann distribution
    4. Equipartition and virial theorems
    5. Diatomic molecules
    6. Virial expansion for fluids
  7. Bose systems
    1. Thermodynamics of ideal Bose systems
    2. Bose-Einstein condensation
    3. Superfluidity
  8. Fermi systems
    1. Thermodynamics of ideal Fermi systems
    2. Degenerate Fermi systems
      1. Electron gas
      2. Atomic nuclei
      3. White dwarf stars
    3. Superconductivity