Effective fluctuation theorems for electron transport in a double quantum dot coupled to a quantum point contact

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD)
capacitively coupled to a quantum point contact (QPC) for the measurement of the DQD charge state. Starting
from a Hamiltonian model, a master equation is obtained for the stochastic process taking place in the DQD while
the QPC is at or away from equilibrium, allowing us to study the measurement back-action of the QPC onto the
DQD. The QPC is treated nonperturbatively in our analysis. Effective fluctuation theorems are established for
the full counting statistics of the DQD current under different limiting conditions. These fluctuation theorems
hold with respect to an effective affinity characterizing the nonequilibrium environment of the DQD and differing
from the applied voltage if the QPC is out of equilibrium. The effective affinity may even change its sign if the
Coulomb drag of the QPC reverses the DQD current. The thermodynamic implications of the effective fluctuation
theorems are discussed.