Role of measurement-feedback separation in autonomous Maxwell's demons

We introduce an information heat engine that is autonomous (i.e., without any time-dependent parameter) but has separated measurement and feedback processes. This model serves as a bridge between the other types of information heat engines inspired by Maxwell's demon; from the original Szilard-engine type systems to the autonomous demonic setups. By analyzing our model on the basis of a general framework introduced in our previous paper [N. Shiraishi and T. Sagawa, Phys. Rev. E {\bf 91}, 012130 (2015).], we clarify the role of the separation of measurement and feedback in the integral fluctuation theorems.