Free energy and phase transitions

Free energy from total entropy, equilibrium and the chemical potential, phase coexistence, Clausius–Clapeyron, nucleation, and metastability.

Where thermodynamics gives the rules of bookkeeping, free energy gives the rule of prediction: the function whose minimum picks out the equilibrium state of a system in contact with its surroundings, whose curvature settles its stability, and whose barriers govern the rate of change between competing phases.

• 4.1 Why free energy: system and reservoir — the total-entropy argument, $F = U - TS$ and $G$, and free energies as Legendre transforms.
• 4.2 Equilibrium, the chemical potential, and stability — equilibrium as a minimum, stability as curvature, the chemical potential, and equal-$\mu$ coexistence.
• 4.3 Phase transitions and coexistence — first-order transitions, latent heat, and the phase diagram.
• 4.4 The Clausius–Clapeyron relation — the slope of a coexistence curve, $dp/dT = L/(T\Delta v)$, and the vapour-pressure curve.
• 4.5 Nucleation and the free-energy barrier — volume gain versus surface cost, the critical radius, and the barrier height.
• 4.6 Metastability and two-state systems — supercooling, the spinodal, and the sigmoidal two-state population.