Money, information and heat in social networks dynamics

Abstract

We propose an information theoretic model for sociological networks that includes money transfer. The model is a microcanonical ensemble of states and particles. The states are the possible pairs of nodes (i.e. people, sites and alike) which exchange information. The particles are the information bits, which may interpreted as money. In this case money transfer is simulated by bits transfer which is heat (energy). With analogy to bosons gas, we define for these networks’ model: 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 T_H and T_C, and we remove Q bits (money) from the hot network to the cold network, we can save W profit bits. The profit will be calculated from W< Q (1-T_H/T_C), namely, Carnot formula. In addition, it is shown that when two of these networks are merged the entropy increases. This explains the tendency of economic and social networks to merge.