  The discovery of unconventional superconductivity in the heavy-fermion
material UTe$_2$ has reinvigorated research of spin-triplet superconductivity.
We perform a theoretical study of coupled two-component spin-triplet
superconducting order parameters and their thermodynamic transitions into the
superconducting state. With focus on the behavior of the temperature dependence
of the specific heat capacity, we find that two-component time-reversal
symmetry breaking superconducting order may feature vanishing or even negative
secondary specific heat anomalies. The origin of this unusual specific heat
behavior is tied to the non-unitarity of the composite order parameter.
Additionally, we supply an analysis of the topological surface states
associated with the different possible spin-triplet orders: single-component
orders host Dirac Majorana surface states in addition to possible bulk nodes. A
second component breaking time-reversal symmetry gaps these surface states
producing chiral Majorana hinge modes. DFT+$U$ band-structure calculations
support that these topological phases are realized in UTe$_2$ when introducing
weak superconducting pairing. Our topological analysis suggests measurable
signatures for surface-probe experiments to acquire further evidence of the
superconducting pairing symmetry.
