  Bosonic gases coupled to a particle reservoir have proven to support a regime
of operation where Bose-Einstein condensation coexists with unusually large
particle-number fluctuations. Experimentally, this situation has been realized
with two-dimensional photon gases in a dye-filled optical microcavity. Here, we
investigate theoretically and experimentally the open-system dynamics of a
grand canonical Bose-Einstein condensate of photons. We identify a regime with
temporal oscillations of the second-order coherence function $g^{(2)}(\tau)$,
even though the energy spectrum closely matches the predictions for an
equilibrium Bose-Einstein distribution and the system is operated deeply in the
regime of weak light-matter coupling. The observed temporal oscillations are
attributed to the nonlinear, weakly driven-dissipative nature of the system
which leads to time-reversal symmetry breaking.
