  We consider non-equilibrium evolution of non-Gaussian fluctuations within
relativistic hydrodynamics relevant for the QCD critical point search in
heavy-ion collision experiments. We rely on the hierarchy of relaxation time
scales, which emerges in the hydrodynamic regime near the critical point, to
focus on the slowest mode such as the fluctuations of specific entropy, whose
equilibrium magnitude, non-Gaussianity and typical relaxation time are
increasing as the critical point is approached. We derive evolution equations
for the non-Gaussian correlators of this diffusive mode in an arbitrary
relativistic hydrodynamic flow. We compare with the simpler case of the
stochastic diffusion on a static homogeneous background and identify terms
which are specific to the case of the full hydrodynamics with pressure
fluctuations and flow.
