## Systems with interactions that decay weakly with distance

### Public lecture of Prof. Stefano Ruffo

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 at the origin of ensemble inequivalence, which in turn implies that specific heat can be negative in the microcanonical ensemble, temperature jumps may appear at microcanonical first order phase transitions, ergodicity is tipically broken. From the dynamical point of view, these systems can be trapped in long-lived quasi-stationary states whose lifetime diverges with system size, hindering relaxation to equilibrium. The approaches recently developed to treat such systems rely on large deviations, Legendre-Fenchel transforms and on kinetic theory. Methods and results in this field are potentially of interest also outside physics.

*A. Campa, T. Dauxois, D. Fanelli and S. Ruffo, "Physics of systems with long-range interactions", Oxford University Press (2014).*