  Disordered hyperuniform structures are locally random while uniform like
crystals at large length scales. Recently, an exotic hyperuniform fluid state
was found in several non-equilibrium systems, while the underlying physics
remains unknown. In this work, we propose a non-equilibrium
(driven-dissipative) hard-sphere model and formulate a hydrodynamic theory
based on Navier-Stokes equations to uncover the general mechanism of the
fluidic hyperuniformity (HU). At a fixed density, this model system undergoes a
smooth transition from an absorbing state to an active hyperuniform fluid, then
to the equilibrium fluid by changing the dissipation strength. We study the
criticality of the absorbing phase transition. We find that the origin of
fluidic HU can be understood as the damping of a stochastic harmonic oscillator
in $q$ space, which indicates that the suppressed long-wavelength density
fluctuation in the hyperuniform fluid can exhibit as either acoustic
(resonance) mode or diffusive (overdamped) mode. Importantly, our theory
reveals that the damping dissipation and active reciprocal interaction
(driving) are two ingredients for fluidic HU. Based on this principle, we
further demonstrate how to realize the fluidic HU in an experimentally
accessible active spinner system and discuss the possible realization in other
systems.
