Evolutionary Dynamics of Large Systems
Several socially and economically important real-world systems comprise large numbers of interacting constituent entities. Examples include the World Wide Web and Online Social Networks (OSNs). Developing the capability to forecast the macroscopic behavior of such systems based on the microscopic interactions of the constituent parts is of considerable economic importance.
Previous researchers have investigated phenomenological forecasting models in such contexts as the spread of diseases in the real world and the diffusion of innovations in the OSNs. The previous forecasting models work well in predicting future states of a system that are at equilibrium or near equilibrium. However, forecasting non-equilibrium states – such as the transient emergence of hotspots in web traffic – remains a challenging problem. In this thesis we investigate a hypothesis, rooted in Ludwig Boltzmann's celebrated H-theorem, that the evolutionary dynamics of a large system – such as the World Wide Web – is driven by the system's innate tendency to evolve towards a state of maximum entropy.
Whereas closed systems may be expected to evolve towards a state of maximum entropy, most real-world systems are not closed. However, the stipulation that if a system is closed then it should asymptotically approach a state of maximum entropy provides a strong constraint on the inverse problem of formulating the microscopic interaction rules that give rise to the observed macroscopic behavior. We make the constraint stronger by insisting that, if closed, a system should evolve monotonically towards a state of maximum entropy and formulate microscopic interaction rules consistent with the stronger constraint.
We test the microscopic interaction rules that we formulate by applying them to two real world phenomena: the flow of web traffic in the gaming forums on Reddit and the spread of Covid-19 virus. We show that our hypothesis leads to a statistically significant improvement over the existing models in predicting the traffic flow in gaming forums on Reddit. Our interaction rules are also able to qualitatively reproduce the heterogeneity in the number of COVID-19 cases across the cities around the globe. The above experiments provide supporting evidence for our hypothesis, suggesting that our approach is worthy of further investigation.
In addition to the above stochastic model, we also study a deterministic model of attention flow over a network and establish sufficient conditions that, when met, signal imminent parabolic accretion of attention at a node