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

TL;DR

This paper reviews the equilibrium and out-of-equilibrium phase transitions in systems with long-range interactions, highlighting recent classifications, new phase transitions, and discussing ongoing challenges in understanding these complex systems.

Contribution

It provides a comprehensive overview of classical and recent results on phase transitions in long-range interacting systems, including new classifications and unobserved phenomena.

Findings

Classification of equilibrium phase transitions

Discovery of a new unobserved equilibrium phase transition

Discussion of out-of-equilibrium phase transitions

Abstract

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.