"Entropy in systems with long-range interactions"

Thierry Dauxois

ENS-Lyon

We will discuss several interesting and unusual features of the entropy of

systems with long-range interactions. In particular, we will present examples

of non concave entropies leading to ensemble inequivalence, and cases of

ergodicity breaking. We will also present a method which uses large deviation

techniques to solve models with long-range interactions in the microcanonical

and canonical ensemble. Several model Hamiltonians will be solved: with

discrete or continuous state variables, with infinite range or slowly decreasing

interactions.