Maximization of entropy in a two layer asymmetry-coupled network

More real-world complex systems contain mass of data and are composed of not only a single layer network. A fundamental problem on these systems is how to get maximum information entropy but economizing energy. Here we explore this problem on a two layer asymmetry-coupled network. On the assumption that a node could couple with more than one counterparts on the other layer network, we found for a given average degree, the entropy of the system varies differently according to the influence coefficient of asymmetry depending on the number of node´s counterparts. We also show that the energy expanded increase if nodes have fewer counterparts or in a not obvious community structure of each layer network, which give a clue to maximizing entropy while consuming least energy on this two layer asymmetry-coupled network.