  In the present work we are studying a bosonic quantum field system at finite
temperature, and at zero and non-zero chemical potential. For a simple spatial
partition we derive the corresponding mutual information, a quantity that
measures the total amount of information of one of the parts about the other.
In order to find it, we first derive the geometric entropy corresponding to the
specific partition and then we substract its extensive part which coincides
with the thermal entropy of the system. In the case of non-zero chemical
potential, we examine the influence of the underlying Bose-Einstein
condensation on the behavior of the mutual information, and we find that its
thermal derivative possesses a finite discontinuity at exactly the critical
temperature.
