  We show that an equilibriumlike additivity property can remarkably lead to
power-law distributions observed frequently in a wide class of
out-of-equilibrium systems. The additivity property can determine the full
scaling form of the distribution functions and the associated exponents. The
asymptotic behavior of these distributions is solely governed by branch-cut
singularity in the variance of subsystem mass. To substantiate these claims, we
explicitly calculate, using the additivity property, subsystem mass
distributions in a wide class of previously studied mass aggregation models as
well as in their variants. These results could help in the thermodynamic
characterization of nonequilibrium critical phenomena.
