Abstract
Nanotechnology has not only provided us the possibility of developing quantum machines but also noncanonical power sources able to drive them. Here we focus on studying the performance of quantum machines driven by arbitrary combinations of equilibrium reservoirs and a form of engineered reservoirs consisting of noninteracting particles but whose distribution functions are nonthermal. We provide the expressions for calculating the maximum efficiency of those machines without needing any knowledge of how the nonequilibrium reservoirs were actually made. The formulas require the calculation of a quantity that we term entropy current, which we also derive. We illustrate our methodology through a solvable toy model where heat "spontaneously" flows against the temperature gradient.
Highlights
The tendency toward miniaturization reached nanoscale a long time ago. This opened up the door to the design and control of different forms of quantum machines, such as quantum motors, quantum pumps, quantum heat engines, or quantum heat pumps 1–15
These systems have been extensively studied during past years, including their dynamical and thermodynamical aspects
The same is true for Tc,l, which presents resonances at ε3 and ε4 and where |ε3 − ε4| Γ we will consider that transmittances are one at their peaks, and that Γ is much smaller than the details of the distribution functions fc, fh, and fl
Summary
The tendency toward miniaturization reached nanoscale a long time ago This opened up the door to the design and control of different forms of quantum machines, such as quantum motors, quantum pumps, quantum heat engines, or quantum heat pumps 1–15. We focus on a somewhat simpler kind of engineered reservoir that we call nonequilibrium incoherent reservoirs (NIRs)[29] These reservoirs consist of noninteracting quantum particles (just as the usual ones in quantum transport7,8,10,12,13), but with distribution functions that are nonthermal. We discuss the thermodynamics and the efficiency of this class of devices but from a description that only requires the probability distribution function of the NIRs. Our formulation is based on the calculation of a quantity that we dubbed entropy current, which here is derived within a semiclassical approach. See Appendix A for an alternative derivation based on von Neumann entropy
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