Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously...

Area of Science:

• Biophysics
• Ecology
• Neuroscience
• Systems Biology

Background:

• Prominent scientific fields study interacting systems coupled to dynamic environments.
• Previous work separated linear interactions and switching environments in mutual information.
• Generalizing these findings is crucial for understanding complex systems.

Purpose of the Study:

• To generalize previous findings on mutual information to nonlinear interacting models.
• To quantify the interplay between nonlinear interactions and environmental changes.
• To investigate the impact of equilibrium versus out-of-equilibrium environments on information.

Main Methods:

• Developed a generalized theoretical framework for nonlinear interacting systems.
• Analyzed mutual information to identify new terms quantifying interaction-environment interplay.
• Extended the framework to continuously varying environments.

Main Results:

• A novel term in mutual information quantifies nonlinear interaction and environmental change interplay, causing constructive or destructive interference.
• Out-of-equilibrium environments yield higher mutual information than equilibrium scenarios.
• Continuously varying environments can be mapped to effective spatially varying diffusion coefficients.

Conclusions:

• The study provides a unified framework for understanding information processing in complex systems with nonlinear interactions and dynamic environments.
• Findings offer insights into biophysical systems in inhomogeneous media.
• Highlights the importance of environmental dynamics in information encoding.