Statistical Mechanics, Physics 971 (Wysin)
Kansas State University, Fall 2020.

Overview:

The course is intended for graduate students in physics who have already had an introductory (undergraduate level) course in thermal physics and thermodynamics, at the level of texts like:

Thermal Physics, by C. Kittel and H. Kroemer, W. H. Freeman, New York, (1980);
Thermodynamics and an Introduction to Thermostatistics, by H. B. Callen, John Wiley & Sons (1985).
An Introduction to Thermal Physics, by Daniel V. Schroeder, Addison-Wesley, (2000).

The presentation here is at the graduate physics level. The student is expected to have a fairly good grasp of many of the basic concepts of thermodyanics, as well probability theory, and an aquaintence with classical mechanics (coordinates, momenta, Hamiltonian, Lagrangians) and quantum mechanics (states, energy levels, degeneracy, Schrödinger equation, eigenvalues).

For more course information, including style of homework submission and grading,
go here: Fall 2020 Physics 971 Syllabus.

Prof. Gary M. Wysin, wysin@phys.ksu.edu.
Office hours: Remotely by appointment, email & via zoom.

Copyright 2020 (Gary M. Wysin) as to this website contents, including the syllabus, exams, problems and lecture notes. See syllabus for further legal statements about the course and its content.

Textbooks

The textbook for the course is the well-known book by Pathria and Beale,

Statistical Mechanics, Third Edition, by R.K. Pathria & Paul D. Beale, Elsvier, Ltd., (2011).

This book is very good but you may find that you have to read between the lines and fill in a lot of the details of the calculations. Also, the writing is very full (perhaps too many words, 733 pages!) so please alot sufficient time for reading carefully.

Other Useful Textbooks

There are too many other texts that may be more concise and somewhat lower level, but possibly from a different perspective, such as.

Fundamentals of Thermal and Statistical Physics, by F. Reif, McGraw-Hill, New York, (1965).
Also wordy but clear explanations. Mix of undergrad and grad level topics.

Statistical Mechanics, by Donald A. McQuarrie, University Science Books (2000).
Much more concise than Pathria, clear shorter explanations, but geared more towards chemistry.

Statistical Thermodynamics, by Lukong Cornelius Fai & Gary Matthew Wysin, CRC Press (2012).
Gives longer explanations of the postulates and connection from statistices to thermodynamics, includes an introduction to path integrals.

Lecture Notes

Scanned images of some of my lecture notes.
  1.     Intro & Review: Range of topics and thermo and math/physics brief reviews
  2.     Chapter 1: Connecting statistics to thermodynamics
  3.     Chapter 2: Ensemble theory, especially, microcanonical and state counting.
  4.     Chapter 3: Canonical ensemble, probabilities, partition function, fluctuations.
  5.     Chapter 3: Canonical ensemble, equipartition, oscillators, paramagnetism.
  6.     Chapter 3: Inverse Laplace transform of Q(β) to get density of states g(E).
  7.     Chapter 3: Canonical ensemble, magnetism and negative temperature, heat flow.
  8.     Chapter 3: Overviews of canonical, isothermal/isobaric, and grand canonical ensembles.
  9.     Chapter 4: Grand canonical ensemble, particle and energy fluctuations, phase equlibrium.
  10.     Chapter 5: Formulation of QM statistics and density matrix.
  11.     Chapter 5: Density matrix examples; Systems with identical particles--bosons, fermions.
  12.     Chapter 5: QM states of free particles in infinite sized systems, δ(r-r') normalization.
  13.     Chapter 6: Statistics for ideal gases & occupation numbers.
  14.     Chapter 6: Kinetic pressure and effusion of gases through a small hole.
  15.     Chapter 6: Gases with internal degrees of freedom; chemical equilibrium.
  16.     Chapter 7: Ideal Bose gases and Bose-Einstein condensation.
  17.     Chapter 7: Ideal Bose gases; blackbody radiation and vibrations in solids.
  18.     Chapter 8: Ideal Fermi gases; thermodynamics at weak and strong degeneracy.
  19.     Chapter 8: Ideal Fermi gases; Pauli paramagnetism and Landau diamagnetism.
  20.     Chapter 8: Ideal Fermi gases: Stellar thermodynamics in white dwarf stars.
  21.     Chapter 8: Ideal Fermi gases: Electron gas in metals; Thomas-Fermi model for atoms.
  22.     Chapter 10: Statistics of cluster expansions for nonideal gases.
  23.     Chapter 12: Phase transitions: Van der Waals gas, Ising model and mean-field theory.
  24.     Chapter 12: Lattice gas and binary alloys; Ising model in the Bethe approximation.
  25.     Chapter 12: Critical behavior & exponents; Landau theory and fluctuations.
  26.     Chapter 12: Exact solution of 1D Ising model by transfer matrix method.

  27.     Physics: NIST 2018 Values of fundamental physical constants.
  28.     Mathematics: Exponential and Gaussian integrals in statistical mechanics.
  29.     Thermodynamics: Speed of sound in fluids and adiabatic compressibility κS.

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    Last update: Wednesday November 11 2020.
    email to --> wysin@phys.ksu.edu