Incomplete information and fractal phase space

Abstract

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $ω$ 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 $ω$ on the basis of fractal phase space. $ω$ 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.