  Many work extraction or information erasure processes in the literature
involve the raising and lowering of energy levels via external fields. But even
if the actual system is treated quantum mechanically, the field is assumed to
be classical and of infinite strength, hence not developing any correlations
with the system or experiencing back-actions. We extend these considerations to
a fully quantum mechanical treatment, by studying a spin-1/2 particle coupled
to a finite-sized directional quantum reference frame, a spin-l system, which
models an external field. With this concrete model together with a bosonic
thermal bath, we analyse the back-action a finite-size field suffers during a
quantum-mechanical work extraction process, the effect this has on the
extractable work, and highlight a range of assumptions commonly made when
considering such processes. The well-known semi-classical treatment of work
extraction from a pure qubit predicts a maximum extractable work W = kT log 2
for a quasi-static process, which holds as a strict upper bound in the fully
quantum mechanical case, and is only attained in the classical limit. We also
address the problem of emergent local time-dependence in a joint system with
globally fixed Hamiltonian.
