  Motivated by the importance of entanglement and correlation indicators in the
analysis of quantum systems, we study the equilibrium and the bipartite
residual entropy in a two-species Bose Hubbard dimer when the spatial phase
separation of the two species takes place. We consider both the zero and
non-zero-temperature regime. We present different kinds of residual entropies
(each one associated to a different way of partitioning the system), and we
show that they strictly depend on the specific quantum phase characterizing the
two species (supermixed, mixed or demixed) even at finite temperature. To
provide a deeper physical insight into the zero-temperature scenario, we apply
the fully-analytical variational approach based on su(2) coherent states and
provide a considerably good approximation of the entanglement entropy. Finally,
we show that the effectiveness of bipartite residual entropy as a critical
indicator at non-zero temperature is unchanged when considering a restricted
combination of energy eigenstates.
