Systems with long-range interactions, like gravitational, charged and dipolar systems, can be made extensive, but are intrinsically non additive. The violation of this basic property of thermodynamics is the origin of many intriguing phenomena in statistical equilibrium. However, even more interesting is the process of relaxation to equilibrium, which is characterized by time-scales that diverge with system size. It has been shown for specific models that the system remains trapped in quasi-stationary states that persist on times that diverge algebraically with the number of particles. Different theoretical approaches have been developed to justify the presence of these states, all of them based on kinetic equations where mean-field effects play a relevant role.

Université de Florence