Free energy from nonequilibrium work: ⟨e^{-βW}⟩ = e^{-βΔF} — exact even for fast, irreversible protocols
Jarzynski 1997: ⟨e^{-βW}⟩ = e^{-βΔF} [exact, any protocol speed]
Crooks FT: P_F(W)/P_R(-W) = e^{β(W-ΔF)} [fluctuation theorem]
Second law: ⟨W⟩ ≥ ΔF → dissipated work Wdiss = ⟨W⟩ - ΔF ≥ 0
Model: particle in double-well V(x), pulled by moving trap λ(t)=vt, friction γ