In recent years, scientists from mathematical disciplines have been able to make forays into the modelling and understanding of a wide array of systems outside the original remit of the physical sciences, including economic problems and the social sciences. The theory of complex networks, in particular, has undergone an exciting development and has now found applications in a wide range of fields, including transport problems in modeling traffic systems, disease spreading or models for modeling agents acting in online communities. Such modelling is at its best if “microscopic”’, agent based models allow for an understanding of the emergence of complex phenomena from simple behavioural rules of the actors. Such emergence in socio-economic systems is almost always an effect of  non-equilibrium phenomena, be it the traffic flow in complex transport networks, the historical development of myths and legends, or the evolution of languages and dialects.

Applications of statistical mechanics as the ones outlined above offer outstanding opportunities for transdisciplinary interactions towards closing the gap between science and the humanities. They are likely to be among the core problems investigated by statistical physicists in the upcoming decades. We suggest to focus on the following subject areas: modelling and understanding of human transport, linguistics and language development, mythology and the analysis of narratives, and election models, government and organisation. Important advances have been made from the side of the analytical sciences in these fields. It is now important to steer these efforts to optimise outcomes and, in particular, involve researchers from the humanities and social sciences more directly in these efforts.