Testing the violation of the Clausius inequality in nanoscale electric circuits

The Clausius inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed, and the possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures where the effect should be visible and that a part of the proposal has already been confirmed.