This paper outlines the applications of one- and two-parameter Poisson- Dirichlet distributions to describe stationary statistical distributions of clusters of agents by types. We discuss how the notion of residudal allocation processes in statistics and population genetics literature also arises as stickbreaking processes in the physics literature. The phenomena of self-(non-) averaging in the physics literature are analogous to long-run non-vanishing of profits or variances of capital sizes in some disequilibrium economic dynamics. We offer an economic interpretation of the physical notion of nonself- averaging as something that refers to the existence of long-run disequilibrium phenomena in economics, rather than thermodynamic limits in statistical physics, since both involve non-vanishing of variances as the size or the time goes to infinity