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.