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We study the equivalence between the recently proposed finite environmentquantum jump model and a master equation approach. We derive microscopicallythe master equation for a qubit coupled to a finite bosonic environment andshow that the master equation is equivalent with the finite environment quantumjump model. We analytically show that both the methods produce the same momentsof work when the work is defined through the two-measurement protocol excludingthe interaction energy. However, when compared to the work moments computedusing the power operator approach, we find a difference in the form of the workmoments. To numerically verify our results, we study a qubit coupled to anenvironment consisting of ten two-level systems.

Comparison between quantum jumps and master equation in the presence of a finite environment