Microcanonical phase transitions for the vortex system

TL;DR

This paper investigates the thermodynamic behavior of vortex systems in bounded domains, revealing multiple phase transitions and entropy convexity in specific geometric configurations.

Contribution

It introduces a variational approach to analyze phase transitions in vortex systems within complex domain geometries, especially near dumbbell shapes.

Findings

Multiple first-order phase transitions can occur in certain domains.

Entropy remains convex at high energy levels.

The system's thermodynamic properties depend on domain shape.

Abstract

We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of ensembles does not hold. For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit an arbitrary number of fist-order phase transitions, while the entropy is convex for large energy.