We present a study of exclusion processes on networks as models for complex transport phenomena and in particular for active transport of motor proteins along the cytoskeleton. We argue that active transport processes on networks spontaneously develop density heterogeneities at various scales. These heterogeneities can be regulated through a variety of multi-scale factors, such as the interplay of exclusion interactions, the non-equilibrium nature of the transport process and the network topology. We show how an effective rate approach allows to develop an understanding of the stationary state of transport processes through complex networks from the phase diagram of one single segment. For exclusion processes we rationalize that the stationary state can be classified in three qualitatively different regimes: a homogeneous phase as well as inhomogeneous network and segment phases. In particular, we present here a study of the stationary state on networks of three paradigmatic models from non-equilibrium statistical physics: the totally asymmetric simple exclusion process, the partially asymmetric simple exclusion process and the totally asymmetric simple exclusion process with Langmuir kinetics. With these models we can interpolate between equilibrium (due to bi-directional motion along a network or infinite diffusion) and out-of-equilibrium active directed motion along a network. The study of these models sheds further light on the emergence of density heterogeneities in active phenomena.
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