A general kinetic theory of liquids I. The molecular distribution functions

TLDR

The authors propose a general kinetic theory of liquids intended to serve as a foundational framework for analyzing all equilibrium and dynamical properties of liquid systems. They introduce multiform distribution functions, derive generalized continuity equations and equations of motion, and obtain integral equations—including a generalized radial distribution function equation—to determine these functions. The theory reproduces Boltzmann’s kinetic equation for gases as a special case and yields equilibrium results consistent with statistical mechanics.

Abstract

This paper outlines a general theory whose object is to provide a basis from which all the equilibrium and dynamical properties of liquids can be investigated. A set of multiform distribution functions is defined, and the generalized continuity equations satisfied by these functions are derived. By introducing the equations of motion, a set of relations is obtained from which the distribution functions may be determined. It is shown that Boltzmann’s equation in the kinetic theory of gases follows as a particular case, and that, in equilibrium conditions, the theory gives results consistent with statistical mechanics. An integral equation for the radial distribution function is obtained which is the natural generalization of one obtained by Kirkwood for ‘rigid spherical molecules’. Finally, it is indicated how the theory may be applied to solve both equilibrium and dynamical problems of the liquid state.