  Complex systems are characterized by multiple spatial and temporal scales. A
natural framework to capture their multiscale nature is that of multilayer
networks, where different layers represent distinct physical processes that
often regulate each other indirectly. We model these regulatory mechanisms
through triadic higher-order interactions between nodes and edges. In this
work, we focus on how the different timescales associated with each layer
impact their effective couplings in terms of their mutual information. We
unravel the general principles governing how such information propagates across
the multiscale structure, and apply them to study archetypal examples of
biological signaling networks and effective environmental dependencies in
stochastic processes. Our framework generalizes to any dynamics on multilayer
networks, paving the way for a deeper understanding of how the multiscale
nature of real-world systems shapes their information content and complexity.
