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Heat transport in quantum devices

Heather Leitch

Published Oct 1, 2026• 0 citations
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Abstract

We use the theory of open quantum systems to study quantum thermal machines, deriving their master equations to understand how they evolve in time. We consider three different working substances coupled to heat baths that may act as engines, refrigerators, accelerators or dissipators. The first is a network of driven quantum harmonic oscillators where we study the effect that the driving speed has on the operation of the system. We see how squeezing one of the baths may lead to a more efficient engine as well as the generation of entanglement within the system. We then investigate the use of coherence in the baths as a resource to improve the performance of a quantum thermal machine whose working substance consists of a single qubit. Finally, we introduce a rotor to a system of two qubits to create an autonomous quantum machine capable of converting heat flow into useful mechanical work. We also study both the heat and angular momentum rectification that may be accomplished by this machine.

DOI
10.17034/32635167

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We use the theory of open quantum systems to study quantum thermal machines, deriving their master equations to understand how they evolve in time. We consider three different working substances coupled to heat baths that may act as engines, refrigerators, accelerators or dissipators. The first is a network of driven quantum harmonic oscillators where we study the effect that the driving speed has on the operation of the system. We see how squeezing one of the baths may lead to a more efficient engine as well as the generation of entanglement within the system. We then investigate the use of coherence in the baths as a resource to improve the performance of a quantum thermal machine whose working substance consists of a single qubit. Finally, we introduce a rotor to a system of two qubits to create an autonomous quantum machine capable of converting heat flow into useful mechanical work. We also study both the heat and angular momentum rectification that may be accomplished by this machine.
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or more baths at different temperatures and continuously driven. To this end, we investigate parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and power of the working device, which can operate as an engine, refrigerator, or accelerator, and analyze the instantaneous and average efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to a dissipator. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
The study of quantum thermodynamics is key to the development of quantum thermal machines. Here we investigate a system of parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and work power of the working device which can operate as an engine or a refrigerator and analyse their instantaneous and averages efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to an accelerator or a heater. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
We investigate the thermodynamics of a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modeling the dynamics and the resulting steady state of the system using a collision model, we identify the functioning of the device as a thermal engine, a refrigerator, or an accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier and optimize both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification, which may be employed to control work extraction through an external load.
The concept of thermal machines has evolved from the canonical steam engine to the recently proposed nanoscopic quantum systems as working fluids. The latter obey quantum open system dynamics and frequently operate in nonequilibrium conditions. However, the role of this dynamics in the overall performance of quantum heat engines remains an open problem. Here we analyze and optimize the efficiency and power output of two-stage quantum heat engines fueled by nonequilibrium steady states. In a charging first stage, the quantum working fluid consisting of a qutrit or two coupled qubits is connected to two reservoirs at different temperatures, which establish a heat current that stores ergotropy in the system; the second stage comprises a coherent driving force that extracts work from the machine in finite a amount of time; finally, the external drive is switched off and the machine enters a new cycle.
The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introduction to the physics of quantum absorption machines, covering refrigerators, engines and clocks in detail.
Abstract We study the thermodynamic performance of a finite-time non-regenerative quantum Stirling-like cycle used as a heat engine. We consider specifically the case in which the working substance (WS) is a two-level system (TLS). The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the WS is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the real-time dynamics of a driven open quantum system with arbitrary fast driving. Following the real-time dynamics of the WS using this master equation, the endpoints of the isotherms can deviate from the equilibrium thermal states. The role of this deviation in the performance of the heat engine is addressed. We found that the finite-time dynamics and thermodynamics of the cycle depend non-trivially on the different time scales at play. In particular, driving the WS at a time scale comparable to the resonance time of the bath enhances the performance of the cycle and allows for an efficiency higher than the efficiency of the quasistatic cycle, but still below the Carnot bound. However, by adding thermalization of the WS with the baths at the end of compression/expansion processes one recovers the conventional scenario in which efficiency decreases by speeding up the processes. In addition, the performance of the cycle is dependent on the compression/expansion speeds asymmetrically, which suggests new freedom in optimizing quantum heat engines. The maximum output power and the maximum efficiency are obtained almost simultaneously when the real-time endpoints of the compression/expansion processes are considered instead of the equilibrium thermal endpoint states. However, the net extractable work always declines by speeding up the drive.