  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). 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 backaction of the QPC onto the DQD. The
QPC is treated non-perturbatively 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.
