On a Model for Integrated Information

TL;DR

This paper thoroughly presents and generalizes a model for integrated information, measuring how system parts causally generate information beyond their individual contributions, and proves it is null for disconnected systems.

Contribution

It offers a comprehensive presentation and a more general formulation of Tononi's integrated information model, applicable across different time scales and initial distributions.

Findings

Integrated information is null for disconnected systems.

Provides a generalized, time-independent formulation of the model.

Clarifies the causal information generation in complex systems.

Abstract

In this paper we give a thorough presentation of a model proposed by Tononi et al. for modeling \emph{integrated information}, i.e. how much information is generated in a system transitioning from one state to the next one by the causal interaction of its parts and \emph{above and beyond} the information given by the sum of its parts. We also provides a more general formulation of such a model, independent from the time chosen for the analysis and from the uniformity of the probability distribution at the initial time instant. Finally, we prove that integrated information is null for disconnected systems.