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We derive the optimal estimates of the free energies of an arbitrary numberof thermodynamic states from nonequilibrium work measurements; the work dataare collected from forward and reverse switching processes and obey afluctuation theorem. The maximum likelihood formulation properly reweights allpathways contributing to a free energy difference, and is directly applicableto simulations and experiments. We demonstrate dramatic gains in efficiency bycombining the analysis with parallel tempering simulations for alchemicalmutations of model amino acids.Comment: 4 pages; to appear in Phys Rev Let

Optimal Estimates of Free Energies from Multistate Nonequilibrium Work Data