Finite-power performance of quantum heat engines in linear response

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Power statistics of Otto heat engines with the Mpemba effect

The Mpemba effect is a counterintuitive relaxation phenomenon whereby a system with a higher initial temperature may cool down to the thermal state faster than an identical system that was initially prepared at a lower temperature. Here, we investigate heat and work in a Markovian state transition system with cyclic switching hot-cold temperatures, which operates as an Otto heat engine working in long but finite time, either with or without the Mpemba effect. Under the condition of the periodic steady state having been reached, the time durations of the heating and cooling relaxation processes are determined by exploring a distance-from-equilibrium equivalent to the Kullback-Leibler divergence. We then numerically evaluate and compare the averages and variances of both the work and the power output of two scenarios with and without the Mpemba effect. The results show that the Markovian Mpemba effect can enhance the machine performance by significantly increasing the power output for a given efficiency without sacrificing the stability.

Finite-time performance of a single-ion quantum Otto engine

We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.

Quantum Otto engine working with interacting spin systems: Finite power performance in stochastic thermodynamics

A quantum Otto engine using two-interacting spins as its working medium is analyzed within framework of stochastic thermodynamics. The time-dependent power fluctuations and average power are explicitly derived for a complete cycle of engine operation. We find that the efficiency and power fluctuations are affected significantly by interparticle interactions, but both of them become interaction-independent under maximal power via optimizing the external control parameter. The behavior of the efficiency at maximum power is further explained by analyzing the optimal protocol of the engine.

Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit

At the classical limit, a multi-stage, endoreversible Carnot cycle model of quantum heat engine (QHE) working with non-interacting harmonic oscillators systems is established in this paper. A simplified combined cycle, where all sub-cycles work at maximum power output (MPO), is analyzed under two types of combined form: constraint of cycle period or constraint of interstage heat current. The expressions of power and the corresponding efficiency under two types of combined constrains are derived. A general combined cycle, in which all sub-cycles run at arbitrary state, is further investigated under two types of combined constrains. By introducing the Lagrangian function, the MPO of two-stage combined QHE with different intermediate temperatures is obtained, utilizing numerical calculation. The results show that, for the simplified combined cycle, the total power decreases and heat exchange from hot reservoir increases under two types of constrains with the increasing number (N) of stages. The efficiency of the combined cycle decreases under the constraints of the cycle period, but keeps constant under the constraint of interstage heat current. For the general combined cycle, three operating modes, including single heat engine mode at low “temperature” (SM1), double heat engine mode (DM) and single heat engine mode at high “temperature” (SM2), appear as intermediate temperature varies. For the constraint of cycle period, the MPO is obtained at the junction of DM mode and SM2 mode. For the constraint of interstage heat current, the MPO keeps constant during DM mode, in which the two sub-cycles compensate each other.

Finite-time performance of a quantum heat engine with a squeezed thermal bath

We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures β_{h} and β_{c}(>β_{h}) with (k_{B}≡1)β=1/T. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as η_{mp}=(η_{C}^{gen})^{2}/[η_{C}^{gen}-(1-η_{C}^{gen})ln(1-η_{C}^{gen})], where the generalized Carnot efficiency η_{C}^{gen} in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter γ: η_{C}^{gen}=1-β_{h}/[β_{c}cosh(2γ)]. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.