Fluctuation theorem in the quantum Otto engine with long-range interaction

The fluctuation of the quantum Otto engine has recently received a lot of attention, while applying the many body with a long-range interaction to a quantum heat engine may enhance our ability of controlling it. Using the two-point measurement and its generalization, we explore the fluctuation theorem of work and heat in a single stroke as well as in a cycle. We discover that the fluctuations of work in a cycle as well as fluctuations of heat in a single stroke or cycle can be connected to the fluctuation of work in a single stroke. Then we numerically investigate the effect of a long-range interaction on these fluctuation theorems, and our result shows that the fluctuation can be improved by manipulating the long-range interaction.