Uhlenbeck G.E., Ford G.W. Lectures in Statistical Mechanics

American Mathematical Society, 1963. — 181 p.These lectures were given by one of us (G. E. U.) as a part of the summer symposium in theoretical physics, which was organized by the American Mathematical Society at the University of Colorado in the summer of 1960. The lectures are printed here almost in the same form as they were presented, which explains the rather colloquial style and the perhaps excessive use of the first personal pronoun. This last feature does not mean that the content of the lectures is due only to the first author. All lectures were thoroughly discussed and prepared by both of us, and most of the developments for which some originality may be claimed are the result of the collaboration of the two authors during many years.
George E. Uhlenbeck
George W. FordThe Explanation of the Laws of Thermodynamics.The Liouville theorem.
The approach to equilibrium: the ideas of Boltzmann.
The generalization by Gibbs. The ergodic theorems.
The laws of thermodynamics.
The notion of temperature. The canonical ensemble.
The first law of thermodynamics.
The second law of thermodynamics.
Notes on Chapter I.
Theory of the Non-Ideal Gas.
The general problem.
The theory of van der Waals.
The Mayer trick and the connection with the theory of linear graphs.
Some notions of the theory of linear graphs.
The first Mayer theorem.
The Mayer equations.
The second Mayer theorem.
The convergence question and the Gaussian model.
Notes on Chapter II.
Remarks on the Condensation Problem.The Van Hove theorem.
The ideas or Yang and Lee.
Some examples.
Notes on Chapter III.
The Boltzmann Equation.The approach to equilibrium.
The linearized Boltzmann equation.
Notes on Chapter IV.
The Propagation of Sound.The Wang-Chang method.
The Kac successive approximation idea.
The Laplace transform method.
The normal mode method.
Notes on Chapter V.
The Chapman-Enskog Development.The general conservation laws.
The Chapman-Enskog development.
Solution of the integral equation (9).
Higher approximations; general form of the development.
The character of the Chapman-Enskog development.
Notes on Chapter VI.
The Kinetic Theory of Dense Gases.
Introduction; the problem of deriving the Boltzmann equation.
The B-B-G-K-Y hierarchy.
The idea of Bogoliubov.
Determination of the functionals Fs.
The kinetic equation.
Discussion of the kinetic equation.
Remarks on the theory of the hydrodynamical stage.
Notes on Chapter VII.
Appendix: Quantum Statistics of Interacting Particles [by Elliott W. Montroll].
The partition function.
Perturbation theory.
Algorithm for construction of integrals associated with diagrams.
Applications to an assembly of charged particles.