  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.
