Statistical mechanics describes physical systems with a huge number of particles. The microscopic description of a system involves the position and momentum of each individual particle. The macroscopic description of the system is given by Thermodynamics, and involves only a few parameters such as temperature, pressure, etc... Statistical Mechanics relates both descriptions, and gives a meaning to notions such as temperature or entropy.
First we will define the three different models to be considered throughout the course: Classical particles satisfying Newton or Hamilton laws of evolution; classical lattice models; and quantum particles satisfying Schroedinger equation. We will define Boltzmann entropy, and prove that it has the right properties as suggested by Thermodynamics.
In the second half of the course we will introduce specific models, such as Ising. They play a considerable role in Physics, and many interesting properties can be mathematically established.
References:
David Ruelle, Statistical Mechanics: Rigorous Results, World Scientific, 1999.
Teunis C. Dorlas, Statistical Mechanics, IOP, 1999.
Kerson Huang, Statistical Mechanics, John Wiley, 1987.
H. B. Callen, Thermodynamics, John Wiley, 1960.