Jarzynski Equality (1997): ⟨e^{-W/kT}⟩ = e^{-ΔF/kT}
Even for arbitrarily fast switching protocols, the exponential average of work equals the exact equilibrium free energy difference. By Jensen's inequality: ⟨W⟩ ≥ ΔF (second law). The dissipated work W_diss = ⟨W⟩ − ΔF ≥ 0.
Rare trajectories where W < ΔF carry disproportionate exponential weight and encode ΔF. Faster switching → broader work distribution → more second-law violations needed for accuracy. This is modeled as a particle dragged in a harmonic potential by a moving trap.