Is there any reason to believe that this intuition works for other complex systems? And does it work using real data (our proofs do require the correlation matrices to have a spectral radius < 2)?

Surprisingly, yeah it works!

Theo. 2: if a OU process with N=3 is synergistic, then interactions must be antibalanced

Theo. 3: antibalanced interaction motifs are necessary for OU processes to be synergy-dominated

For any strength of interactions, here are some numerical results when N = 8 (using every possible sign pattern):

First, we used the O-information and (social) structural balanced theory to show that the O-information can be expanded in terms of closed walks in the correlation matrix Σ.

The terms that contribute synergistically are exactly the kind of walks that you would find in antibalanced graphs!

Around Falmer, photo taken by Simon Bowes

Between Brighton and Clayton, on the A23