Analysis of complexity in interacting diffusion systems by entropy characteristic

We investigate a class of systems with finite-capacity effect which has a more complex configuration than a well-known diffusion process featured by random walk. To answer how complex such a diffusion process is, entropy rate is introduced. Systems with finite-capacity effect are characterized by variable capacity of routers locating on highly heterogeneous complex networks. It is shown that the combinational behavior of complex topology and variable capacity is the main origin of complexity described by positive entropy. Further, analytical expressions are derived and convinced by simulations. Also, Maximum entropy principle provides an effective measure to design an optimal diffusion process.