Generalized active information: extensions to unbounded domains

TL;DR

This paper extends the concept of active information to unbounded domains, allowing complexity measures based on disequilibrium from maximum entropy to be applied beyond finite spaces.

Contribution

It generalizes active information to unbounded domains, broadening its applicability to complexity measures in infinite or unbounded spaces.

Findings

Active information can be evaluated in unbounded support baselines.

The extension allows for complexity measures beyond finite spaces.

The approach maintains the interpretability of disequilibrium from maximum entropy.

Abstract

In the last three decades, several measures of complexity have been proposed. Up to this point, most of such measures have only been developed for finite spaces. In these scenarios the baseline distribution is uniform. This makes sense because, among other things, the uniform distribution is the measure of maximum entropy over the relevant space. Active information traditionally assumes a finite interval universe of discourse but can be extended to other cases where maximum entropy is defined. Illustrating this is the purpose of this paper. Disequilibrium from maximum entropy, measured as active information, can be evaluated from baselines with unbounded support.