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Biochemistry, ecology, and neuroscience are examples of prominent fieldsaiming at describing interacting systems that exhibit non-trivial couplings tocomplex, ever-changing environments. We have recently shown that linearinteractions and a switching environment are encoded separately in the mutualinformation of the overall system. Here, we first generalize these findings toa broad class of non-linear interacting models. We find that a new term in themutual information appears, quantifying the interplay between non-linearinteractions and environmental changes, and leading to either constructive ordestructive information interference. Furthermore, we show that a higher mutualinformation emerges in out-of-equilibrium environments with respect to anequilibrium scenario. Finally, we generalize our framework to the case ofcontinuously varying environments. We find that environmental changes can bemapped exactly into an effective spatially-varying diffusion coefficient,shedding light on modeling and information structure of biophysical systems ininhomogeneous media.

Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities