  We report the numerical observation of a far-from-equilibrium equation of
state (EoS) in the Gross-Pitaevskii model. This universal dimensionless EoS is
constructed by relating the turbulent cascade's scale-free spectrum amplitude
to the energy flux of the steady state that emerges from the large-length-scale
driving of a Bose-Einstein condensate (BEC). Remarkably, this EoS defies the
generic predictions of wave-turbulent kinetic theory, even though the cascade
spectra are quantitatively well understood within that theory. Finally, we find
that the concept of quasi-static thermodynamic processes between equilibrium
states extends to far-from-equilibrium steady states.
