Derivation of quantum master equation with counting fields by monitoring a probe

We show a microscopic derivation of a quantum master equation with counting terms which describes the electron statistics. A localized spin behaves as a probe whose precession angle monitors the net electron current by the magnetic-moment interaction. The probe Hamiltonian is proportional to the current, and is determined self-consistently for a model of a quantum dot. Then it turns out that the quantum master equation for the spin-precession contains the counting terms. As an application, we show the fluctuation theorem for the electron current.Comment: 7 page

Universal Lower and Upper Bounds of Efficiency of Heat Engines from Thermodynamic Uncertainty Relation

According to Thermodynamics, the efficiency of a heat engine is upper bounded by Carnot efficiency. For macroscopic systems, the Carnot efficiency is, however, achieved only for quasi static processes. And, considerable attention has been paid to provide general evaluation of the efficiency at a finite speed. Recently, several upper bounds of the efficiency have been derived in the context of the trade-off among the efficiency, power, and other quantities such as the fluctuation of power. Here, we show universal lower and upper bounds of the efficiency from the thermodynamic uncertainty relations for the entropy production and for the heat transfers. The lower bound is characterized by the ratio between the fluctuation of the irreversible entropy production and mean output work. The upper bound of the efficiency is described by a generalized precision of the heat transfers among the working substance, and hot and cold reservoirs. We explicitly derive necessary and sufficient conditions of both the lower and upper bounds in a unified manner in terms of fluctuation theorem. Hence, our result provides an operating principle of the heat engine.Comment: 6 pages, 4figure