2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215076Based on the general analysis of the grand canonical partition function in the S-matrix framework, the calculated results on symmetry energy, free energy and entropy of dilute warm nuclear matter are presented. At a given temperature and density, the symmetry energy or symmetry free energy of the clusterized nuclear matter in the S-matrix formulation deviates, particularly at low temperature and relatively higher density, in a subtle way, from the linear dependence on the square of the isospin asymmetry parameter $X=(ρ_n-ρ_p)/(ρ_n+ρ_p)$, contrary to those obtained for homogeneous nucleonic matter. The symmetry coefficients, in the conventional definition, can then be even negative. The symmetry entropy similarly shows a very different behavior.8 pages, 6 figures. PRC (in press)Nuclear Theorytext