Many applications require knowledge of the free energy, but its calculation by work-based methods is notoriously prone to inaccuracy. We discuss a conceptual basis for understanding this behavior, and ways to detect and remedy it. We then describe applications to crystal phases, where sampling and free-energy calculations can be improved by exploiting the approximate harmonic character of the crystal. We then examine developments in the field obtained through the use of the Transition-Matrix Monte Carlo methods, presented in the context of mixtures, and finally we examine how some of the foregoing ideas can be applied to evaluate thermodynamic phase coexistence.
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