Simple Discrete Systems
– Microstates and macrostates.
– The N-coin model, probabilities of microstates and macrostates with fair coins,

prob(n) = Ω(N) / Ω(all),   with   Ω(n) = (N choose n).

– The N-spin paramagnet, counting microstates corresponding to a macrostate.
– The Einstein model of a solid, N oscillators, each with energy equal to a multiple of hf,

Ω(N, q) = (q+N–1 choose q).

The Ideal Gas
– Setting up the calculation of the multiplicity of microstates for given N and U,

Ω(N,U) = f(N) V ^N U ^3N/2.

– Gaussian form of the multiplicity Ω(N_A,U_A; N_B,U_B) for fixed U = U_A + U_B.

Statistical Mechanics, Heat Flow and the Second Law
– The fundamental assumption of statistical mechanics.
– Behavior of Ω_total = Ω_AΩ_B for a system consisting of subsystems A and B.
– The second law of thermodynamics in terms of multiplicities, statistical origin.

Entropy
– Small, large, and very large numbers; Stirling's approximation,

N! = N ^N e^–N (2πN)^1/2   and    ln N! = N ln N – N.

– Concept and definition of entropy,

S = k ln Ω.

– The second law of thermodynamics in terms of entropy.
– Entropy growth, reversible and irreversible processes.
– Calculating S starting from in examples, including entropy of mixing.