Statistical physics of network structure and information dynamics

In the last two decades, network science has proven to be an invaluable tool for the analysis of empirical systems across a wide spectrum of disciplines, with applications to data structures admitting a representation in terms of complex networks. On the one hand, especially in the last decade, an increasing number of applications based on geometric deep learning have been developed to exploit, at the same time, the rich information content of a complex network and the learning power of deep architectures, highlighting the potential of techniques at the edge between applied math and computer science. On the other hand, studies at the edge of network science and quantum physics are gaining increasing attention, e.g., because of the potential applications to quantum networks for communications, such as the quantum Internet. In this work, we briefly review a novel framework grounded on statistical physics and techniques inspired by quantum statistical mechanics which have been successfully used for the analysis of a variety of complex systems. The advantage of this framework is that it allows one to define a set of information-theoretic tools which find widely used counterparts in machine learning and quantum information science, while providing a grounded physical interpretation in terms of a statistical field theory of information dynamics. We discuss the most salient theoretical features of this framework and selected applications to protein-protein interaction networks, neuronal systems, social and transportation networks, as well as potential novel applications for quantum network science and machine learning.