Nonuniform classical fluid mixture in one-dimensional space with next neighbor interactions

Abstract

An overcomplete description is used to represent thermodynamic potentials, for a one-dimensional classical fluid mixture with next neighbor interaction, in compact closed form. In descriptions of this class, a thermodynamic potential depends not only on minimally sufficient control variables, but on others as well with respect to which it is stationary. Here, this is done first in the direct, or fugacity-controlled format, with the grand potential as the relevant generating function. It is then transcribed to an indirect, relative density functional format, with overcompleteness restricted to a set of grand potential densities. Poly-dispersity requires a separate treatment. Extensions outside of the range of strict one-dimensionality are discussed, as are several approximation methods.