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

TL;DR

This paper generalizes the understanding of mutual information in complex systems, revealing how non-linear interactions, out-of-equilibrium conditions, and continuously changing environments influence information encoding and system behavior.

Contribution

It introduces a new term in mutual information accounting for non-linear interactions and environmental changes, and maps environmental variations to an effective diffusion coefficient.

Findings

A new mutual information term quantifies interaction-environment interplay.

Higher mutual information is observed in out-of-equilibrium environments.

Environmental changes can be modeled as spatially-varying diffusion coefficients.

Abstract

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.