A Structure behind Primitive Chaos

TL;DR

This paper uncovers a hierarchical structure within primitive chaos, showing how new chaos and causality can emerge from existing chaos through a recursive process involving coarse graining, with implications for understanding fundamental physical concepts.

Contribution

It reveals a hidden hierarchical structure in primitive chaos, demonstrating how new chaos and causality can be constructed from existing chaos via recursive procedures.

Findings

A recursive method to construct new primitive chaos from existing chaos.

Identification of conditions necessary for primitive chaos to exhibit hierarchical structure.

Insights into the essential conditions and chaotic behaviors of primitive chaos.

Abstract

Recently, a new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. {\bf 79}, 15002 (2010)]. This letter reveals a structure hidden behind the primitive chaos; under some conditions, a new primitive chaos is constructed from the original primitive chaos, this procedure can be repeated, and the hierarchic structure of the primitive chaos is obtained. This implies such a picture that new events and causality is constructed from the old ones, with the aid of the concept of a coarse graining. As an application of this structure, interesting facts are revealed for the essential condition of the primitive chaos and for the chaotic behaviors.