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The evaluation of entropy is an important topic in relation to the direction of spontaneous change. A variety of methods for the calculation of the entropy and free energy have been proposed. However, the calculation of the entropy through computer simulation has posed difficulties because the entropy is not a mechanical property but a statistical property. The difficulties are related to large fluctuations attendant upon the averages of the Boltzmann factors. The particle insertion (PI) method provides a simple way of calculating chemical potentials. In this method, the excess chemical potential μ ex is expressed as

Direct and Highly Efficient Estimation of the Entropy through the Canonical Ensemble Average of Acceptance Ratios