Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer

We study the fluctuation theorem in single-electron sequential tunneling regime. We consider single-electron transport through a double quantum dot (DQD) monitored by a capacitively coupled quantum point-contact (QPC) electrometer. In this setup it is possible to perform a direction resolved real-time electron counting experiment. We derive the full counting statistics for the coupled DQD - QPC system and obtain the joint probability distribution of the charges transferred through the DQD and the QPC. We show that the joint probability distribution satisfies the fluctuation theorem for 4-terminal system. For two-terminal DQD, the effective temperature should be introduced to recover the fluctuation theorem. The system can be described by a master equation with tunneling rates depending of the counting fields and satisfying a generalized local detailed-balance relation. Furthermore, we derive universal relations between the non-linear corrections to the current and noise, which can be verified in experiment.