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

Thermal Equilibrium in D-dimensions: From Fluids and Polymers to Kinetic Wealth Exchange Models