Estimating errors in free energy calculations from thermodynamic integration using fitted data.

A procedure to estimate the statistical uncertainties associated with free energies computed from thermodynamic integration using fitted data is described. The method involves generating synthetic data sets from the actual simulation data and performing an analysis of the resulting distribution of free energy values. These values follow a Gaussian distribution, and the corresponding standard deviation is associated with the error in the computed value of the free energy. The impact of these uncertainties on the coexistence pressure is examined for first-order transitions. The approach is demonstrated with an examination of finite-size effects at the freezing transition of hard spheres.