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 the 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 first-order phase transitions, while the entropy is convex for large energy.

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