Now we modify the theoretical scheme allowing for the transition rates to be computed with help of the P(E)-theory. We saw that the P(E)-theory relates the transition rates with a function \(J(t)\) that accounts for the coupling of the system and the environment. Indeed, in our system the drag subsystem is coupled to the drive subsystem. Then, the latter can be considered as “the environment” and therefore, the transition rates for the drag system needs to computed with a P(E)-theory that includes the noise voltage fluctuations of the drive subsystem. Similarly one could also “exchanged” the roles of drag and drive subsystems and get transition rates for the new drag subsystem also modified by the voltage noise in the drive subsystem. However, the fact of considering the noise fluctuations in the P(E)-theory is rather complicated at this stage. As a preliminary attempt we consider that indeed the environment that both dots see are “resistors” which means that now the P(E) transistion rates looks: \[P(E)=\frac{1}{\sqrt{4\pi E_C \kappa^2 k_BT}}e^{-(E-\kappa^2 k_B T)^2/(4\kappa^2 E_C k_B T)}\] Where \(E_C\) is the Coulomb energy for the two dot system which is a combination among the individual capacitances \(C_{i}\) and the interdot capacitative coupling. In order to see how this function depends on the system parameters as the temperature and the charging energy we below plot \(P(E)\) for some cases