Entropy Production in Stationary Social Media Networks

Completing their initial phase of rapid growth social media networks are expected to reach a plateau from where on they are in a statistically stationary state. Such stationary states may have different dynamical properties. For example, if each message in a network is followed by a reply in opposite direction, the dynamics is locally balanced. Otherwise, if messages are ignored or forwarded to a different user, one may reach a stationary state with a directed flow of information. To distinguish between the two situations, we propose a quantity called entropy production that was introduced in statistical physics as a measure for non-vanishing probability currents in nonequilibrium stationary states. We present a general scheme that allows one to measure the entropy production in arbitrary communication networks and demonstrate its application in a specific example.