  Considering the thermodynamics of bosons in a lattice described by the
Bose-Hubbard Hamiltonian, we report the occurrence of anomalous double peaks in
their specific heat dependence on temperature. This feature, usually associated
with a high geometrical frustration, can also be a consequence of a purely
energetic competition. By employing self-energy functional calculations
combined with finite-temperature perturbation theory, we propose a mechanism
based on ground-state degeneracies expressed as residual entropies. A general
decomposition of the specific heat regarding all possible transitions between
the system's eingenvalues provides an insight into the nature of each maximum.
Furthermore, we address how the model parameters modify the structure of these
peaks based on its spectral properties and atom-atom correlation function.
