  In this paper we discuss some examples of systems composed of $N$ units,
which exchange a conserved quantity $x$ according to some given stochastic
rule, from some standard kinetic model of condensed matter physics to the
kinetic exchange models used for studying the wealth dynamics of social
systems. The focus is on the similarity of the equilibrium state of the various
examples considered, which all relax toward a canonical Gibbs-Boltzmann
equilibrium distribution for the quantity $x$, given by a $\Gamma$-distribution
with shape parameter $\alpha = D/2$, which implicitly defines an effective
dimension $D$ of the system. We study various systems exploring (continuous)
values of $D$ in the interval $[1,\infty)$.
