Compute free energy differences ΔF using thermodynamic integration: ΔF = ∫₀¹ ⟨∂H/∂λ⟩_λ dλ. Compare with Bennett Acceptance Ratio and Jarzynski equality. Visualize hysteresis and work distributions.
Thermodynamic integration: ΔF_AB = ∫₀¹ ⟨∂H_λ/∂λ⟩_λ dλ where H_λ=(1-λ)H_A+λ·H_B. Jarzynski equality (1997): e^{-W/kT} = e^{-ΔF/kT} — exact even far from equilibrium! Bennet acceptance ratio (BAR): optimal estimator for ΔF. Free energy perturbation (FEP/MBAR): used in drug discovery for binding affinity calculations. These are the gold standard for alchemical transformations in biomolecular simulation.