  We illustrate recent results concerning the validity of the work fluctuation
theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi,
Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable
model of an open quantum system. The central role played by the thermodynamic
partition function of the open quantum system, -- a two level fluctuator with a
strong quantum nondemolition coupling to a harmonic oscillator --, is
elucidated. The corresponding quantum Hamiltonian of mean force is evaluated
explicitly. We study the thermodynamic entropy and the corresponding specific
heat of this open system as a function of temperature and coupling strength and
show that both may assume negative values at nonzero low temperatures.
