  We study the thermodynamic properties of the Bose-Einstein condensate (BEC)
in the context of the quantum field theory with non-commutative target space.
Our main goal is to investigate in which temperature and/or energy regimes the
non-commutativity can characterize some influence in the BEC properties
described by a relativistic massive non-commutative boson gas. The
non-commutativity parameters play a key role in the modified dispersion
relations of the non-commutative fields, leading to a new phenomenology. We
have obtained the condensate fraction, internal energy, pressure and specific
heat of the system and taken ultra-relativistic (UR) and non-relativistic
limits (NR). The non-commutative effects in the thermodynamic properties of the
system are discussed. We found that there appear interesting signatures around
the critical temperature.
