Mutual information disentangles internal interactions from changing environments

Real-world systems are characterized by complex interactions among their internal degrees of freedom while living in ever-changing environments whose net effect is to act as additional couplings. Here, we study a paradigmatic interacting model in a switching, but unobserved, environment. We show that the limiting properties of the mutual information of the system allow for a disentangling of these two sources of couplings. Our approach can be extended to a wide class of stochastic dynamics and might stand as a general method to discriminate complex internal interactions from equally complex changing environments.