Statistical theory of nonuniform systems and reduced description in the density fluctuation theory

Abstract

A statistical theory of nonuniform systems is developed, based on the conditional distribution method. Junior correlation functions of a nonuniform system have been used to obtain an explicit expression for the Helmholtz free energy and the effective Hamiltonian as functionals of the particle number density field. The structure of a transient layer at the liquid-gas interface and a surface sorption effect have been studied. A method of reduced description in the fluctuation theory, using the conditional correlation functions of the particle number density distribution, is suggested. An infinite system of integro-differential equations is obtained for the correlation functions introduced. A method for its truncation is proposed. As a result, the grand statistical integral, which takes into account the density field fluctuations of the system in equilibrium with a thermostat, is calculated.