Validity and breakdown of onsager symmetry in mesoscopic conductors interacting with environments

We investigate magnetic-field asymmetries in the linear transport of a mesoscopic conductor interacting with its environment. Interestingly, we find that the interaction between the two systems causes an asymmetry only when the environment is out of equilibrium. We elucidate our general result with the help of a quantum dot capacitively coupled to a quantum Hall conductor and discuss the asymmetry dependence on the environment bias and induced dephasing.