Fig. 3.

Comparison between integrated information and the sum of transfer entropies (TE). A system consists of two binary units whose states are determined by an AND gate and a noisy AND gate. When the noise level of the noisy AND gate is low and thus the dependence between the units is strong, the sum of transfer entropies (green line) exceeds the mutual information (black line) whereas integrated information ${\mathrm{\Phi }}_G$ (red line) is always less than the mutual information. Each transfer entropy (blue solid and dotted lines) is always less than or equal to ${\mathrm{\Phi }}_G$.