Foundations of Equilibrium Statistical Mechanics

Relate phase space, microstates, and macrostates for a classical N-particle system.

Derive Liouville's theorem from Hamilton's equations and interpret its meaning as the incompressibility of the phase-space fluid.

Explain the physical content of the ergodic hypothesis and its role in justifying the replacement of time averages with ensemble averages.

State the fundamental postulate of equal a priori probabilities for an isolated system.

Define the microcanonical ensemble (N, V, E) and derive the Boltzmann entropy S = k_B ln Ω(N, V, E).

Define temperature, pressure, and chemical potential as partial derivatives of entropy in the microcanonical framework.