  We consider a theoretical model of a four-mode Bose-Hubbard model consisting
of two pairs of wells coupled via two processes with two different rates. The
model is naturally divided into two subsystems with strong intra-system
coupling and much weaker coupling between the two subsystems and has previously
been introduced as a model for Josephson heat oscillations by Strzys and Anglin
[\pra {\bf 81}, 043616 (2010) ]. We examine the quantum dynamics of this model
for a range of different initial conditions, in terms of both the number
distribution among the wells and the quantum statistics. We find that the time
evolution is different to that predicted by a mean-field model and that this
system exhibits a wide range of interesting behaviours. We find that the system
equilibriates to a maximum entropy state and is thus a useful model for quantum
thermalisation. As our model may be realised to a good approximation in the
laboratory, it becomes a candidate for experimental investigation.

Quantum Physics;Quantum Gases