Integrated Information and State Differentiation

Integrated information (Φ) is a measure of the cause-effect power of a physical system. This paper investigates the relationship between Φ as defined in Integrated Information Theory and state differentiation ([Formula: see text]), the number of, and difference between potential system states. Here we provide theoretical justification of the relationship between Φ and [Formula: see text] , then validate the results using a simulation study. First, we show that a physical system in a state with high Φ necessarily has many elements and specifies many causal relationships. Furthermore, if the average value of integrated information across all states is high, the system must also have high differentiation. Next, we explore the use of [Formula: see text] as a proxy for Φ using artificial networks, evolved to have integrated structures. The results show a positive linear relationship between Φ and [Formula: see text] for multiple network sizes and connectivity patterns. Finally we investigate the differentiation evoked by sensory inputs and show that, under certain conditions, it is possible to estimate integrated information without a direct perturbation of its internal elements. In concluding, we discuss the need for further validation on larger networks and explore the potential applications of this work to the empirical study of consciousness, especially concerning the practical estimation of Φ from neuroimaging data.