Calculation of Molecular Entropies Using Temperature Integration

There are two fundamental definitions of entropy, Clausius's thermodynamic definition and the Boltzmann-Gibbs statistical mechanical definition. The Clausius definition, applied here to the calculation of molecular entropies, requires an integration over temperature. Analytical and numerical error analysis shows that this quadrature can be done accurately using a small number of large temperature steps involving the calculation of one average system property, the mean internal energy. This makes the method computationally practical for systems with many degrees of freedom, such as biological molecules. The Clausius definition provides a simple and physically insightful way to decompose a total entropy change into components and is useful for benchmarking statistical mechanical based methods for entropy calculation. A temperature quenching protocol is described whereby the Clausius method can be used with existing force fields to evaluate entropy changes in anharmonic and diffusive systems.