Non-equilibrium Statistical Mechanics of Two-dimensional Vortices

TL;DR

This paper demonstrates that two-dimensional vortices do not reach thermodynamic equilibrium but instead form a persistent non-equilibrium stationary state with a predictable core-halo structure, supported by molecular dynamics simulations.

Contribution

It reveals the non-equilibrium stationary state of interacting vortices in the thermodynamic limit and predicts its core-halo structure theoretically.

Findings

Vortices form a non-equilibrium stationary state.

The vortex distribution has a predictable core-halo structure.

Simulations confirm theoretical predictions.

Abstract

It has been observed empirically that two dimensional vortices tend to cluster forming a giant vortex. To account for this observation Onsager introduced a concept of negative absolute temperature in equilibrium statistical mechanics. In this Letter we will show that in the thermodynamic limit a system of interacting vortices does not relax to the thermodynamic equilibrium, but becomes trapped in a non-equilibrium stationary state. We will show that the vortex distribution in this non-equilibrium stationary state has a characteristic core-halo structure, which can be predicted {\it a priori}. All the theoretical results are compared with explicit molecular dynamics simulations.