Statistical mechanics of systems of many interacting agent
Concepts such as order-disorder phase transitions and critical phenomena are by no means confined to physics. Also economies and societies – as systems of many interacting individuals – organize themselves in different macro-states, with different degrees of order (e.g. in terms of coordination on social norms or of trust) or of symmetry (e.g. in terms of predictability in financial markets). The tools of statistical physics can be applied to the characterization of the collective behavior of these systems as well. In particular, the theory of disordered systems allows one to characterize typical properties of systems of heterogeneous agents or of systems with with random interactions. This is relevant, for example, to address issues of systemic stability in financial markets. Likewise, non-equilibrium statistical physics provides tools to characterize socio-economic processes, e.g. coarsening in simple models of residential segregation or of the dynamics of wealth distribution.
Inference in complex systems and large data-set
The IT revolution is providing more and more detailed information on the elementary processes which take place in several complex systems, from cellular functions to financial markets. This calls for methods of feature extraction and inference of a novel type. Concepts derived from statistical physics, such as the entropy of randomized network ensembles, can be used, for example, to estimate the relevance of a given feature (e.g. protein concentration) for the architecture of a specific network (e.g. protein interaction network). In the same spirit, the Von Neumann expanding model allows to characterize the properties of metabolic networks and shed light on the relation between essential genes and reactions whose fluxes are constrained. This general approach finds further application to high frequency financial data and macro-economics.
