The statistical physics of real-world networks: standing on Jaynes’ shoulders*

In 1957 Jaynes proposed an Information Theory approach to derive the statistical ensembles of Statistical Mechanics: the maximisation of the Shannon entropy, after constraining the energy of the system, returns exactly the probability distributions of the canonical ensemble. Otherwise stated, Jaynes’ approach consists in fixing some crucial information regarding the description of the system (i.e. the energy) and then maximising the “ignorance" about the unconstrained degrees of freedom.
Recently, the same approach was extended to the study of complex networks. Analogously, the constraints represent some - local or global - informative quantities for the description of the real system, while all other observables are left completely random. This approach provides a reliable benchmark for the analysis of complex networks, to reconstruct a network from a limited information or to highlight the role of local constraints in the ensemble non equivalence.
In the present seminar I will review the definition and the evolution of such framework and introduce some of its last applications in different fields, as online social networks, economic and financial systems, biological networks.