Nonequilibrium properties of an inhomogeneous electron gas are studied using the method of the nonequilibrium statistical operator by D.N. Zubarev. Generalized transport equations for the mean values of inhomogeneous operators of the electron number density, momentum density, and total energy density for weakly and strongly nonequilibrium states are obtained. We derive a chain of equations for the Green's functions, which connects commutative time-dependent Green's functions "density-density", "momentum-momentum", "enthalpy-enthalpy" with reduced Green's functions of the generalized transport coefficients and with Green's functions for higher order memory kernels in the case of a weakly nonequilibrium spatially inhomogeneous electron gas.

A new approach is proposed to calculate the thermodynamic potential, which consists in reducing the relevant non-Gaussian functional integral to its Gaussian form with a renormalized "density-density" correlator. It is shown that the knowledge of the effective potential of electron-electron interaction is sufficient to calculate the thermodynamic potential in this approach.

An effective potential of electron-electron interaction and a two-particle "density-density" correlator are calculated for semi-infinite jellium. Their asymptotics at large distances between electrons are studied in a plane parallel to the surface.

We present a statistical theory for diffusion-reaction processes of gaseous mixture in the system "metal-adsorbate-gas". The theory is based on an equal consideration of electron-electron, electron-atom and atom-atom interactions between adsorbed, non-adsorbed atoms and atoms of metal surface. On a metal surface, the bimolecular reactions of the A + B ↔ AB type are possible between the adsorbed atoms which is typical of catalytic processes. By means of Zubarev nonequilibrium statistical operator, the system of transport equations is obtained for a consistent description of electronic kinetic and diffusion-reaction atomic processes.

Energy of electronic subsystem of semi-infinite metal is presented in the form of an expansion in powers of pseudo-potential. It is shown that generally electron many-particle density matrices are necessary for the energy calculation, whereas in case of a local pseudo-potential only diagonal elements (electron distribution functions) are necessary. In a specific case of a local pseudo-potential within the first order of perturbation theory, our results for energy coincide with those widely applicable in the density functional theory.