Taking this course is a response to what I realized previous term: I need a proper introduction to equilibrium statistical mechanics. The lecturer, Girma Hailu, followed the textbook Thermal Physics by Charles Kittel very closely, almost religiously. His style is energetic, and his approach is very helpful in guiding students to read through the textbook, which is a classic.
The central concept is entropy. I had wondered why using logarithm in the expression of entropy, and hence one of the most enlightening moment for me is to read the follow:
“The use of logarithm is a mathematical convenience: it is easier to write 10^20, than exp(10^20), and it is more natural for two systems to speak of σ1 + σ2, than of g1g2. “
All the other major concepts follow readily from very simple considerations. For example, temperature is the partial derivative of entropy over energy and gives criteria for energy transfer/equilibrium of systems in thermal contact. Chemical potential is the partial derivative of entropy over number of particles and gives criteria for material transfer/equilibrium of systems in thermal and diffusive contact. Gibbs distribution and Boltzmann distribution followed again from simple applications of chemical potential in a two state system and its classical limit.