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.

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.

Based on the effective Hubbard model we suggest a statistical description of reaction-diffusion processes for bimolecular chemical reactions of gas particles adsorbed on the metallic surface. The system of transport equations for description of particles diffusion as well as reactions is obtained. We carry out the analysis of the contributions of all physical processes to the formation of diffusion coefficients and chemical reactions constants.