Ergotropic advantage in a measurement-fueled quantum heat engine

TL;DR

This paper investigates a quantum heat engine powered by generalized measurements on a coupled two-qubit working medium, introducing a five-stroke cycle that appends an ergotropy-extracting stroke after the measurement. For $z$-$z$ measurements, the engine exhibits positive work output with the ergotropy stage, and a key identity $W_T^{(5)} = W_T^{(4)} + W_T^{(3)}$ emerges, linking the five-, four-, and three-stroke variants. Across other measurement directions, coherence in the post-measurement state can further enhance performance, with weak measurements sometimes outperforming projective ones. The findings highlight a tunable thermodynamic advantage from measurement-induced energy input combined with ergotropy extraction, with feasible experimental implementations in platforms such as NMR and superconducting circuits.

Abstract

This paper investigates a coupled two-qubits heat engine fueled by generalized measurements of the spin components and using a single heat reservoir as sink. Our model extends the proposal of Yi and coworkers [Phys. Rev. E {\bf 96}, 022108 (2017)] where the role of a hot reservoir in a four-stroke cycle was replaced by a quantum measurement apparatus, the other steps being two quantum adiabatic strokes and thermalization with a cold reservoir. We propose a five-stroke cycle, where an ergotropy extracting stroke is introduced following the measurement stroke, and study the effect of measurements of different spin components on the performance of the machine. For measurements along z-z directions, we find two possible occupation distributions that yield an active state and the ergotropic stroke improves the performance of the engine over the four-stroke cycle. Further, the three-stroke engine ( {without the adiabatic strokes}) yields the same performance as the five-stroke engine. For arbitrary working medium and non-selective measurements, we prove that the total work output of a five-stroke engine is equal to the sum of the work outputs of the corresponding four-stroke and three-stroke engines. For measurement directions other than z-z, there may be many possible orderings of the post-measurement probabilities that yield an active state. However, as we illustrate, for specific cases (e.g. x-x), a definite ordering may be obtained with the projective measurements. Thus, we find that the five-stroke engine exploiting ergotropy outperforms both its four-stroke as well as three-stroke counterparts.

Figures (6)

• Figure 1: A five-stroke engine cycle consisting of the first quantum adiabatic stroke ($1\rightarrow2$), the measurement stroke ($2\rightarrow3$), the ergotropy extraction stroke ($3\rightarrow4$), the second quantum adiabatic stroke ($4\rightarrow5$) and finally the thermalization stroke with the heat reservoir ($5\rightarrow1$). Without the stroke $3\rightarrow 4$, the cycle reduces to the four-stroke engine of Ref. YiJ2017.
• Figure 2: R1 case: Heat and work contributions in the five-stroke cycle vs. $c_{0}$. Parameters are set at $B_{1} = 3.5$, $B_{2}$ = 3, $J$ = 1 and $\beta$ = 1.
• Figure 3: R1 case: Efficiency [Eq. (\ref{['eqn89']})] vs. $c_{0} \in [0,1/\sqrt{2}]$. $B_{2} = 3$ and $J = 1$. So, the limiting value of the efficiency (as $\beta \to \infty$) is $B_2/4J = 0.75$.
• Figure 4: R1 case: Efficiency [Eq. (\ref{['eqn89']})] vs. $J$. $B_{2} = 3$ and $c_{0}=0.3$.
• Figure 5: R2 case: Efficiency vs. $c_{0}$. $B_{2} = 3.9$, $J = 1$. The efficiency decreases as the temperature is lowered at a given measurement strength, unlike the R1 case (see Fig. \ref{['fig3']}). The R2 efficiency is also maximized at $c_0=1/2$.