On the nature of time in time-dependent expansionary processes

TL;DR

This paper explores the relationship between process-specific time and a universal measure of time in expansionary processes, using information entropy to analyze how time scales with the growth of the expansion space.

Contribution

It introduces a method to rescale process-specific time to a universal time measure using information entropy in time-dependent expansionary processes.

Findings

Time (t) can be rescaled to a universal time (T) in expansionary processes.

The universal time T is directly related to the information entropy of the process.

Time T correlates with the increase in the size of the expansion space.

Abstract

For an expansionary process, the size of the expansion space will increase. If the expansionary process is time-dependent, time (t) will increase as a function of the increase in the size of the expansion space. A statistical information entropy methodology was used to investigate the properties of time-dependent expansionary processes both in theory and through examples. The primary objective of this paper was to investigate whether there is a universal measure of time (T) and how it relates to process related time (t), that is specific to any given time-dependent expansionary process. It was found that for such time-dependent processes, time (t) can be rescaled to time (T) such that, T and the information entropy (H(T)) of the expansionary process are the same, and directly related to the increase in the size of the expansion space.