  We propose a unified description of two important phenomena: color
confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We
focus on the confinement/deconfinement transition characterized by the increase
of the entropy from $N^0$ to $N^2$, which persists in the weak coupling region.
Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in
gauge theory, and S$_N$ permutations in the system of identical bosons -- is
crucial for the formation of the condensed (confined) phase. We relate standard
criteria, based on off-diagonal long range order (ODLRO) for BEC and the
Polyakov loop for gauge theory. The constant offset of the distribution of the
phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter
for the partially-(de)confined phase at finite coupling. We demonstrate this
explicitly for several quantum mechanical systems (i.e., theories at small or
zero spatial volume) at weak coupling, and argue that this mechanism extends to
large volume and/or strong coupling. This viewpoint may have implications for
confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
