Detection of single-electron heat transfer statistics

We consider a quantum dot system whose charge fluctuations are monitored by a quantum point contact allowing for the detection of both charge and transferred heat statistics. Our system consists of two nearby conductors that exchange energy via Coulomb interaction. In interfaces consisting of capacitively coupled quantum dots, energy transfer is discrete and can be measured by charge counting statistics. We investigate gate-dependent deviations away from a charge fluctuation theorem in the presence of local temperature gradients (hot spots). Non-universal relations are found for state-dependent charge counting. A fluctuation theorem holds for coupled dot configurations with heat exchange and no net particle flow.