Complex systems are characterised by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behaviour. Examples arise both in the physical and non-physical worlds. The study of complex systems forms a new interdisciplinary research area that cuts across physics, biology, ecology, economics, sociology, and the humanities. In this paper we review the essence of complex systems from a physicists' point of view, and try to clarify what makes them conceptually different from systems that are traditionally studied in physics. Our goal is to demonstrate how the dynamics of such systems may be conceptualised in quantitative and predictive terms by extending notions from statistical physics and how they can often be captured in a framework of co-evolving multiplex network structures. We mention three areas of complex-systems science that are currently studied extensively, the science of cities, dynamics of societies, and the representation of texts as evolutionary objects. We discuss why these areas form complex systems in the above sense. We argue that there exists plenty of new ground for physicists to explore and that methodical and conceptual progress is needed most.

We consider the problem of two-point resistance in a resistor network previously studied by one of us (Wu 2004 J. Phys. A: Math. Gen. 37 6653). By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the resistance between two nodes in the network. Particularly, our results prove a recently proposed conjecture on the resistance between the center node and a node on the network boundary. Our analysis also solves the spanning tree problem on the cobweb network.

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur