Entropy current and efficiency of quantum machines driven by nonequilibrium incoherent reservoirs

TL;DR

This paper develops a theoretical framework to evaluate the efficiency of quantum machines powered by nonthermal, nonequilibrium reservoirs, introducing the concept of entropy current and demonstrating its application in a solvable model.

Contribution

It introduces a method to calculate maximum efficiency of quantum machines with engineered reservoirs without detailed reservoir construction knowledge.

Findings

Derived formulas for maximum efficiency using entropy current.

Showed heat flow against temperature gradient in a toy model.

Provided a practical approach for analyzing quantum machine performance.

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.