Abstract
Explosive astrophysical systems - such as supernovae or compact star binary mergers - provide conditions where exotic degrees of freedom can be populated. Within the covariant density functional theory of nuclear matter we build several general purpose equations of state which, in addition to the baryonic octet, account for $\Delta(1232)$ resonance states. The thermodynamic stability of $\Delta$-admixed nuclear matter is investigated in the limiting case of vanishing temperature for charge fractions $Y_Q=0.01$ and $Y_Q=0.5$ and wide ranges of the coupling constants to the scalar and vector mesonic fields. General purpose equation of state models with exotica presently available on the \textsc{CompOSE} database are further reviewed; for a selection of them we then investigate thermal properties for thermodynamic conditions relevant for core-collapse supernovae and binary neutron star mergers. Modifications induced by hyperons, $\Delta(1232)$, $K^-$, pions and quarks are discussed.
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