  We consider bosons in a harmonic trap and investigate the fluctuations of the
work performed by an adiabatic change of the trap curvature. Depending on the
reservoir conditions such as temperature and chemical potential that provide
the initial equilibrium state, the exponentiated work average (EWA) defined in
the context of the Crooks relation and the Jarzynski equality may diverge if
the trap becomes wider. We investigate how the probability distribution
function (PDF) of the work signals this divergence. It is shown that at low
temperatures the PDF is highly asymmetric with a steep fall off at one side and
an exponential tail at the other side. For high temperatures it is closer to a
symmetric distribution approaching a Gaussian form. These properties of the
work PDF are discussed in relation to the convergence of the EWA and to the
existence of the hypothetical equilibrium state to which those thermodynamic
potential changes refer that enter both the Crooks relation and the Jarzynski
equality.
