Toward the construction of the entropic-force model of the expansion of the Universe due to the gravitationally-induced production of dark matter and the influence of exchange entropy on the event horizon

Within the framework of Prigogin's gravitational theory of the geometry-matter connection that ensures the production of particles in a cosmological fluid, a single-fluid model of the evolution of a spatially flat, homogeneous and isotropic Universe is thermodynamically constructed. In order to obtain it, the continuity equation (energy conservation equation) was derived from the first law of thermodynamics taking into account the gravity-induced creation of matter and energy exchange processes on the visible horizon of the Universe. Based on this equation and the fundamental Friedman equation describing the expansion of the Universe, in the context of the entropic formalitу modified Friedman-Robertson-Walker equations were constructed to model various scenarios of the evolution of the flat Universe with matter production. In their derivation, several forms of exchangeable phenomenological entropies associated by assumption with the region of the visible cosmological horizon were used. The resulting generalized Prigogine model agrees well with the standard cosmological $\Lambda$-model for cold dark matter and allows us to explain the accelerated expansion of the late Universe, providing its cosmological history without the introduction of new fields.