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We experimentally study emergence of microcanonical equilibrium states in theturbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-signvortices are injected into a quasi-two-dimensional disk-shaped atomicBose-Einstein condensate using a range of mechanical stirring protocols. Theresulting long-time vortex distributions are found to be in excellent agreementwith the meanfield Poisson-Boltzmann equation for the system describing themicrocanonical ensemble at fixed energy $\cal{H}$ and angular momentum$\cal{M}$. The equilibrium states are characterized by the correspondingthermodynamic variables of inverse temperature $\hat{\beta}$ and rotationfrequency $\hat{\omega}$. We are able to realize equilibria spanning the fullphase diagram of the vortex gas, including on-axis states nearzero-temperature, infinite temperature, and negative absolute temperatures. Atsufficiently high energies the system exhibits a symmetry-breaking transition,resulting in an off-axis equilibrium phase at negative absolute temperaturethat no longer shares the symmetry of the container. We introduce apoint-vortex model with phenomenological damping and noise that is able toquantitatively reproduce the equilibration dynamics.

Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas