  The equilibrium statistical mechanics of one-dimensional lattice gases with
interactions of arbitrary range and shape between first-neighbor atoms is
solved exactly on the basis of statistically interacting vacancy particles. Two
sets of vacancy particles are considered. In one set all vacancies are of
one-cell size. In the other set the sizes of vacancy particles match the
separation between atoms. Explicit expressions are obtained for the Gibbs free
energy and the distribution of spaces between atoms at thermal equilibrium.
Applications to various types of interaction potentials are discussed,
including long-range potentials that give rise to phase transitions. Extensions
to hard rod systems are straightforward and are shown to agree with existing
results for lattice models and their continuum limits.
