The functional mechanics: evolution of the moments of distribution function and the Poincare recurrence theorem

TL;DR

This paper explores how functional mechanics bridges classical mechanics and statistical physics by analyzing the evolution of distribution moments, addressing Poincare recurrence paradoxes and showing the destruction of periodicity.

Contribution

It introduces a novel approach to connect classical and statistical mechanics through moments of distribution functions and discusses implications for Poincare recurrence.

Findings

Deviations from classical trajectories are quantified.

Evolution of distribution moments is constructed.

Periodicity of movement is shown to be destroyed.

Abstract

This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. 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 Poincare-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.