  Units of complex systems -- such as neurons in the brain or individuals in
societies -- must communicate efficiently to function properly: e.g., allowing
electrochemical signals to travel quickly among functionally connected neuronal
areas in the human brain, or allowing for fast navigation of humans and goods
in complex transportation landscapes. The coexistence of different types of
relationships among the units, entailing a multilayer represention in which
types are considered as networks encoded by layers, plays an important role in
the quality of information exchange among them. While altering the structure of
such systems -- e.g., by physically adding (or removing) units, connections or
layers -- might be costly, coupling the dynamics of subset(s) of layers in a
way that reduces the number of redundant diffusion pathways across the
multilayer system, can potentially accelerate the overall information flow. To
this aim, we introduce a framework for functional reducibility which allow us
to enhance transport phenomena in multilayer systems by coupling layers
together with respect to dynamics rather than structure. Mathematically, the
optimal configuration is obtained by maximizing the deviation of system's
entropy from the limit of free and non-interacting layers. Our results provide
a transparent procedure to reduce diffusion time and optimize non-compact
search processes in empirical multilayer systems, without the cost of altering
the underlying structure.
