There has been an increasing interest in the quantification of nearlydeterministic work extraction from a finite number of copies of microscopicparticles in finite time. This paradigm, so called single-shotepsilon-deterministic work extraction, considers processes with small failureprobabilities. However, the resulting fluctuations in the extracted workentailed by this failure probability have not been studied before. In thestandard thermodynamics paradigm fluctuation theorems are powerful tools tostudy fluctuating quantities. Given that standard fluctuation theorems areinadequate for a single-shot scenario, here we formulate and prove afluctuation relation specific to the single-shot epsilon-deterministic workextraction to bridge this gap. Our results are general in the sense that weallow the system to be in contact with the heat bath at all times. As acorollary of our theorem we derive the known bounds on theepsilon-deterministic work.
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