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 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 in which the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and a 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 analyze work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations, and we obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.

Automated summary

This study examines work extraction processes of two-level systems mediated by finite-time interactions with an ambient bath, known as partial thermalizations, as continuous-time Markov processes. The research reveals fluctuations in the amount of work that can be extracted due to the stochastic nature of the process, and investigates the impact of the rate at which system parameters are driven and the rate of thermalization with the bath. Analytic expressions for average work and a lower bound for the variance of work are derived, demonstrating that such processes generally cannot be fluctuation-free. Furthermore, the study shows that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynski's fluctuation-dissipation relation and analyzes work extraction cycles under different constraints by modifying the Carnot cycle.