Quantifying nonequlibrium thermodynamic operations in a multiterminal mesoscopic system

We investigate a multiterminal mesoscopic conductor in the quantum Hall regime, subject to temperature and voltage biases. The device can be considered as a nonequilibrium resource acting on a working substance. We previously showed that cooling and power production can occur in the absence of energy and particle currents from a nonequilibrium resource (calling this an N-demon). Here we allow energy or particle currents from the nonequilibrium resource and find that the device seemingly operates at a better efficiency than a Carnot engine. To overcome this problem, we define free-energy efficiencies which incorporate the fact that a nonequilibrium resource is consumed in addition to heat or power. These efficiencies are well behaved for equilibrium and nonequilibrium resources and have an upper bound imposed by the laws of thermodynamics. We optimize power production and cooling in experimentally relevant parameter regimes.