  Interacting systems driven far from equilibrium tend to evolve to steady
states exhibiting large-scale structure and order. In two-dimensional turbulent
flow the seemingly random swirling motion of a fluid can evolve towards
persistent large-scale vortices. Lars Onsager proposed a model based on
statistical mechanics of quantized vortices to explain such behavior. Here we
report the first experimental confirmation of Onsager's model of turbulence. We
drag a grid barrier through an oblate superfluid Bose--Einstein condensate to
generate non-equilibrium distributions of vortices. We observe an inverse
energy cascade driven by the evaporative heating of vortices, leading to
steady-state configurations characterized by negative temperatures. Our results
open a pathway for quantitative studies of emergent structures in interacting
quantum systems driven far from equilibrium.
