On the use of the quasi-Gaussian entropy theory in noncanonical ensembles. II. Prediction of density dependence of thermodynamic properties

A. Amadei, M. E. F. Apol, and H. J. C. Berendsen
Groningen Biomolecular Sciences and Biotechnology Institute (GBB), Department of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

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Abstract

In previous articles we derived and tested the quasi-Gaussian entropy theory, a description of the excess free energy in terms of the potential or full internal energy or enthalpy probability distribution, instead of the (configurational) partition function. We obtained in this way the temperature dependence of thermodynamic functions in the NVT, NpT and µVT ensembles assuming a Gaussian, Gamma or Inverse Gaussian distribution. In this article we extend the theory to describe the density dependence of thermodynamic properties, using the distribution of volume and number of particles in the isothermal-isobaric and grand canonical ensemble, respectively. In both ensembles pressure-density expressions for a Gaussian and various Gamma distributions are derived and applied to water. A Gamma description for the volume distribution turns out to be a good model in the gas range, which is in accordance with the volume distribution of an ideal gas. A Gamma description for the particle number distribution works well for liquid densities.