The Statistical Mechanics of Dynamical Social Networks

We propose an information-theoretic model for sociological networks. Usually, networks are considered as the array of links connecting the net nodes. Here we analyze a dynamical net in which every node is connected to all other nodes and links that randomly move between the pairs of nodes. These nets are similar to i.e. the internet where the sites are the nodes and the transferred bits are the links. The analysis of this net is analogous to a microcanonical ensemble of states and particles. The states are all the possible pairs of nodes (i.e. people, sites, and alike) that exchange particles which in the case of the internet are the information bits. In analogy to boson gas, we define these networks: entropy, volume, pressure, and temperature. We show that these definitions are consistent with Carnot efficiency (the second law) and ideal gas law. Therefore, if we have two large networks: hot and cold having temperatures TH and TC and we remove Q energetic bits from the hot network to the cold network we can save W profit bits that are calculated from the Carnot efficiency. In addition, it is shown that when two dynamical networks are merged the entropy increases. This explains the tendency of economic and social networks to merge. Equilibrium thermodynamics proved to be an important tool in engineering, chemistry, and physics. Applying these tools to sociological network dynamics may prove to be of some use.