Lattice liquid theory of ion-hopping conduction

The theory of ion-hopping conduction in a classical lattice liquid, the interacting lattice gas, in the context of the master equation is developed in terms of newly introduced number operators which are consistent with the lattice gas statistics. An explicit equation of many-body probability thus acquired is utilized in averaging physical quantities. One of the main applications is forwarded to the development of the relaxation mode theory for the noninteracting lattice gas particles on any lattice structure. The other application is to obtain a hierarchy of equations, and to confirm the coupled equations derived from the pair approximation of the path probability method under the nearest-neighbor interaction. The method proceeded in the text holds for the Coulomb interaction case as well.