Non-equilibrium Statistical Mechanics of Two-dimensional Vortices

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.

References in corpus (13)

• Electrostatic correlations: from Plasma to Biology
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Emergence of order from turbulence in an isolated planar superfluid
• Gibbs, Boltzmann, and negative temperatures
• Collisionless relaxation in non-neutral plasmas
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems
• Quasi-stationary states in the self-gravitating sheet model
• Statistical Mechanics of 1d Self-Gravitating Systems: The Core-Halo Distribution
• Vortex Thermometry for Turbulent Two-Dimensional Fluids
• Image Effects on the Transport of Intense Nonaxisymmetric Charged Beams
• Entropy production in systems with long range interactions

Cited by in corpus (12)

• Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas
• The true mechanism of spontaneous order from turbulence in two-dimensional superfluid manifolds
• Universal expansion of vortex clusters in a dissipative two-dimensional superfluid
• Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates
• Origin of Negative Temperatures in Systems Interacting with External Fields
• Hydrodynamic Entropy and Emergence of Order in Two-dimensional Euler Turbulence
• Negative-temperature Fourier transport in one-dimensional systems
• On the 3D turbulence regime in a Tokamak plasma edge
• Linear and non-linear instabilities of Kirchhoff's Elliptical Vortices
• Broken Symmetries in Quasi-2D Charged Systems via Negative Dielectric Confinement
• Two dimensional Coulomb gas in a non-conservative trap
• Predicting the Final Stationary State of Sheared 2D Euler Fluids