Construction of a quantum Carnot heat engine cycle

Abstract

The microscopic state description of an irreversible quantum Carnot cycle for a general quantum working medium is investigated. An efficiency lag term, which quantifies the deviation of the irreversible cycle efficiency from the classical Carnot efficiency, is given in terms of the total entropy increase in the universe. The efficiency lag and the total entropy increase in the universe are directly connected to the quantum relative entropy between the density matrices obtained at the end of the quantum adiabatic and the relaxation steps of the cycle. The total entropy increase and the efficiency lag are found to be always nonnegative quantities. Our results give a direct proof that the irreversible cycle efficiency is always smaller than the classical Carnot efficiency. Two interacting spins under an external magnetic field are proposed as the working medium of the irreversible quantum Carnot cycle. The external magnetic field is considered to be quasistatically changed during the steps of the cycle. The coupling between the spins is found to break down the scale invariance and make the quantum Carnot cycle irreversible. It is shown that while the quantum coupling can lower the cycle efficiency monotonically to zero, it can make the irreversible cycle to produce more work than the one obtained from the uncoupled spins. The conditions in which one can always construct a reversible Carnot cycle for the coupled spin working medium are also given.