The entropy functional, the information path functional's essentials and their connections to Kolmogorov's entropy, complexity and physics

TL;DR

This paper explores the entropy functional and the information path functional, analyzing their relationships with Kolmogorov's entropy, complexity, and physical systems, focusing on their mathematical properties and applications.

Contribution

It introduces recent results on the entropy functional and IPF, studying their singularities, invariant relations, and connections to chaos and complexity in controlled diffusion processes.

Findings

Analysis of singularities of IPF extremal equations

Identification of invariant relations related to IPF

Connections established between entropy functionals and chaos measures

Abstract

The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to the Kolmogorov's entropy, complexity and the Lyapunov's characteristics. Considering the IPF's essentials and specifics, the paper studies the singularities of the IPF extremal equations and the created invariant relations, which both are useful for the solution of important mathematical and applied problems. Keywords: Additive functional; Entropy; Singularities, Natural Border Problem; Invariant