Fluctuation theorems for capacitively coupled electronic currents

The counting statistics of electron transport is studied theoretically in a system with two capacitively coupled
parallel transport channels. Each channel is composed of a quantum dot connected by tunneling to two reservoirs.
The nonequilibrium steady state of the system is controlled by two affinities or thermodynamic forces, each one
determined by the two reservoirs of each channel. The status of a single-current fluctuation theorem is investigated
starting from the fundamental two-current fluctuation theorem, which is a consequence of microreversibility.We
show that the single-current fluctuation theorem holds in the limit of a large Coulomb repulsion between the
two parallel quantum dots, as well as in the limit of a large current ratio between the parallel channels. In this
latter limit, the symmetry relation of the single-current fluctuation theorem is satisfied with respect to an effective
affinity that is much lower than the affinity determined by the reservoirs. This backaction effect is characterized
quantitatively.