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