  Higher order time-correlators of spontaneous spin fluctuations reveal the
information about spin interactions. We argue that in a broad class of spin
systems one can justify a phenomenological approach to explore such
correlators. Thus, we predict that the 3rd and 4th order spin cumulants are
described by a universal function that can be parametrized by a small set of
parameters. We show that the fluctuation theorem constrains this function so
that such correlators are fully determined by lowest nonlinear corrections to
the free energy and the mean and variance of microscopic spin currents. We also
provide an example of microscopic calculations for conduction electrons.
