  We show that a two-atoms Bose-Hubbard model exhibits three different phases
in the behavior of thermal entanglement in its parameter space. These phases
are demonstrated to be traceable back to the existence of quantum phase
transitions in the same system. Significant similarities between the behaviors
of thermal entanglement and heat capacity in the parameter space are brought to
light thus allowing to interpret the occurrence and the meaning of all these
three phases.
