Jarzynski equality ⟨e^{-W/kT}⟩=e^{-ΔF/kT} and Crooks fluctuation theorem. Simulate a particle dragged through a harmonic potential and verify free energy recovery from nonequilibrium work distributions.
Jarzynski (1997): ⟨e^{-W/kT}⟩ = e^{-ΔF/kT} regardless of process speed — exact nonequilibrium free energy from fast pulling! Crooks (1999): P_F(W)/P_R(-W) = e^{(W-ΔF)/kT}. Second law: ⟨W⟩ ≥ ΔF (work always exceeds free energy). Rare events with W<ΔF exponentially dominate Jarzynski average — importance of tails. Applications: protein unfolding (Ritort lab), single-molecule experiments.