Some topological properties of the kinetic modeling of a non-equilibrium system

The topological properties of the kinetic modeling of a non-equilibrium system, which are due to the inhomogeneity of the structure of its energy spectrum, are considered. In particular, it was shown that the layered structure of the energy spectrum of a non-equilibrium system can be interpreted from a topological point of view as the incoherence of the energy spectra of its quasi-equilibrium subsystems. The possibility of using the Riemann and the scalar curvature of the hypersurface of the total entropy production as local and global characteristics of the non-equilibrium state of the system is shown.