  We show that, in conserved-mass transport processes, the steady-state
distribution of mass in a subsystem is uniquely determined from the functional
dependence of variance of the subsystem mass on its mean, provided that joint
mass distribution of subsystems is factorized in the thermodynamic limit. The
factorization condition is not too restrictive as it would hold in systems with
short-ranged spatial correlations. To demonstrate the result, we revisit a
broad class of mass transport models and its generic variants, and show that
the variance of subsystem mass in these models is proportional to square of its
mean. This particular functional form of the variance constrains the subsystem
mass distribution to be a gamma distribution irrespective of the dynamical
rules.
