Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows

Freddy Bouchet (1) , Julien Barré (2) , Antoine Venaille (3)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with many claims, the equilibrium statistical mechanics of such systems is a well understood subject. In this proceeding, we explain briefly the classical approach to equilibrium and non equilibrium statistical mechanics for these systems, starting from first principles. We emphasize recent and new results, mainly a classification of equilibrium phase transitions, new unobserved equilibrium phase transition, and out of equilibrium phase transitions. We briefly discuss what we consider as challenges in this field.

Mots clés: Long range interactions; Inequivalence of ensembles; Kinetic theory; Out of equilibrium phase transitions; Two dimensional turbulence; Geophysical flows

Domaines: Mécanique statistique [cond-mat.stat-mech]; Dynamique des Fluides [physics.flu-dyn]

Freddy Bouchet, Julien Barré, Antoine Venaille. Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows. DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG RANGE INTERACTIONS: Theory and Experiments, Jul 2007, Italy. pp.117-152. ⟨hal-00257073⟩