  We study work extraction processes mediated by finite-time interactions with
an ambient bath -- \emph{partial thermalizations} -- as continuous time Markov
processes for two-level systems. Such a stochastic process results in
fluctuations in the amount of work that can be extracted and is characterized
by the rate at which the system parameters are driven in addition to the rate
of thermalization with the bath. We analyze the distribution of work for the
case where the energy gap of a two-level system is driven at a constant rate.
We derive analytic expressions for average work and lower bound for the
variance of work showing that such processes cannot be fluctuation-free in
general. We also observe that an upper bound for the Monte Carlo estimate of
the variance of work can be obtained using Jarzynski's fluctuation-dissipation
relation for systems initially in equilibrium. Finally, we analyse work
extraction cycles by modifying the Carnot cycle, incorporating processes
involving partial thermalizations and obtain efficiency at maximum power for
such finite-time work extraction cycles under different sets of constraints.
