The Maximum Entropy Principle for Temporal and Ecological Networks: Memory, Fluctuations and Response in Complex Systems

Many real systems, represented using complex networks, of- ten exhibit intrinsic dynamism that uncovers fundamental properties. This thesis explores various aspects of such dy- namism through the lens of maximum entropy formalism, presenting methodologies that effectively characterize and har- ness this aspect. The work is divided into two main parts. The first part devel- ops a novel maximum entropy model to characterize memory effects and structural heterogeneity in temporal networks. This model captures the evolution of network connections over time, focusing on how nodes create and maintain links. Uti- lizing this model, the research uncovers topological patterns, such as community structures, emphasizing the role of mem- ory mechanisms in encoding network properties. The second part shifts focus to ecological networks, empha- sizing system fluctuations for modeling and predictive analy- sis. Here, maximum entropy formalism is shown to be a tool capable of constructing models that incorporate significant fluctuations in system characteristics. These models are then shown to enhance pattern detection, particularly emphasiz- ing the ecological contexts. Finally, I discuss how this approach can be used to define a new perspective on the diversity-stability debate by link- ing entropy with system stability and demonstrating how, through the Fluctuation Response Relation, properly charac- terized fluctuations can predict systems’ response to pertur- bations.