Work fluctuations due to partial thermalizations in two-level systems

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