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

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.

References in corpus (18)

• Estimating Mutual Information
• Weak pairwise correlations imply strongly correlated network states in a neural population
• Statistical mechanics for natural flocks of birds
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• Maximum entropy models for antibody diversity
• Physics of Active Emulsions
• Switching and growth for microbial populations in catastrophic responsive environments
• Estimating Mixture Entropy with Pairwise Distances
• Evolution of a Fluctuating Population in a Randomly Switching Environment
• Diffusion-limited reactions in crowded environments
• Estimation of mutual information for real-valued data with error bars and controlled bias
• Latent dynamical variables produce signatures of spatiotemporal criticality in large biological systems
• Mutual information disentangles interactions from changing environments
• Testing the critical brain hypothesis using a phenomelogical renormalization group
• Coarse-grained entropy production with multiple reservoirs: unraveling the role of time-scales and detailed balance in biology-inspired systems
• Disentangling the critical signatures of neural activity
• Diffusion of tagged particles in a crowded medium
• Information-driven transitions in projections of underdamped dynamics