Effective elementarity of resonances and bound states in statistical mechanics

Operational criteria are presented for determining those bound states and resonances which can approximately be included in the complete set of states in the $S$-matrix formulation of statistical mechanics. The criteria depend only on the energy dependence of $S$-matrix elements, as compared to the energy scales determined by the temperature and density. They are thus expressible free of nonrelativistic potential-theory language, and are hopefully valid for relativistic hadron systems as well. As an application, it is shown that the $\Delta$ resonance can be effectively treated as an elementary species under the temperature and density conditions encountered in neutron stars, while nuclei such as the deuteron can be ignored to lowest approximation. Possible conflicts with the Pauli principle, as invoked between the "constituents" of composite resonances and bound states on the one hand and free particles on the other, are resolved.