The functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem

One of modern approaches to a problem of the coordination of classical mechanics and the statistical physics — the functional mechanics is considered. Deviations from classical trajectories are calculated and evolution of the moments of distribution function is constructed. The relation between the received results and absence of paradox of Poincaré–Zermelo in the functional mechanics is discussed. Destruction of periodicity of movement in the functional mechanics is shown and decrement of attenuation for classical invariants of movement on a trajectory of functional mechanical averages is calculated.