Incomplete information and fractal phase space

TL;DR

This paper explores how incomplete information in complex systems relates to fractal phase space, showing that the incompleteness parameter reflects the fractal dimension and information growth during scale refinement.

Contribution

It establishes a link between the incompleteness parameter and fractal phase space, providing a physical interpretation of the parameter in terms of fractal dimensions.

Findings

The incompleteness parameter $$ is proportional to the fractal dimension.

$$ relates to phase volume expansion during scale refinement.

Information growth correlates with fractal structure in phase space.

Abstract

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of $\omega$ on the basis of fractal phase space. $\omega$ is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process.