Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

Antoine Venaille (1, 2) , Freddy Bouchet (1)

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

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.

Mots clés: Long range interactions; ensemble inequivalence; phase transitions : bicritical points; Fofonoff flows; 2D Euler equation; Quasi-Geostrophic model

Domaines: Mécanique statistique [cond-mat.stat-mech]; Océan, Atmosphère

Antoine Venaille, Freddy Bouchet. Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows. 2007. ⟨hal-00183784⟩