Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2008.07512 · Physical Review A

Stroboscopic two-stroke quantum heat engines

Otavio A. D. Molitor, Gabriel Teixeira Landi

Published Oct 16, 2020• 45 citations
arXivHTMLPDF

Abstract

The formulation of models describing quantum versions of heat engines plays an important role in the quest toward establishing the laws of thermodynamics in the quantum regime. Of particular importance is the description of stroke-based engines, which can operate at finite time. In this paper we put forth a framework for describing stroboscopic, two-stroke engines, in generic quantum chains. The framework is a generalization of the so-called SWAP engine and is based on a collisional model, which alternates between pure heat and pure work strokes. The transient evolution towards a limit cycle is also fully accounted for. Moreover, we show that once the limit cycle has been reached, the energy of the internal sites of the chain no longer changes, with the heat currents being associated exclusively to the boundary sites. Using a combination of analytical and numerical methods, we show that this type of engine offers multiple ways of optimizing the output power, without affecting the efficiency. Finally, we also show that there exists an entire class of models, characterized by a specific type of interchain interaction, which always operate at Otto efficiency, irrespective of the operating conditions of the reservoirs.

DOI
10.1103/physreva.102.042217

Related papers

Máquinas térmicas quânticas em tempo finito.

Otavio A. D. Molitor

In the last decade, the study of thermodynamic phenomena in ultra-small scales, where quantum mechanics becomes imperative, has gained a lot of attention. The possibility of controlling single quantum states in nowadays experimental setups has encouraged a more intense inquiry over the intersection between thermodynamics and quantum mechanics, which is known as quantum thermodynamics. Particularly relevant in this framework is the study of quantum heat engines, that is, quantum systems undergoing thermodynamic cycles. Thermodynamic cycles contain all the aspects of thermodynamics, thus its a good testbed for a better comprehension of the thermodynamics of quantum systems. Moreover, modelling quantum heat engines is crucial for the design of future ultra-small engines. Nonetheless, another aspect must be taken into account, finite-time operation. Its very important for the optimization of the output power of the engine. In this dissertation, we present a new model of finite-time quantum heat engines. By making use of collisional models, we construct a model in which a generic quantum chain experiences sequential pure heat and pure work strokes. Dictated by stroboscopic evolution, the engines state goes through a transient regime until the limit-cycle is reached. After the achievement of the limit-cycle, our results indicate that only the boundary sites of the quantum chain are relevant for the heat currents exchanged with the baths. By means of analytical and numerical methods, we present how the model is useful for optimizing the output power of stroke-based quantum heat engines, without decreasing their respective efficiencies. Lastly, we prove that there is a universal efficiency value, the Otto efficiency, for a whole family of models containing a specific kind of internal interactions. For completeness, other methods from the literature which deal with finite-time quantum heat engines are also presented and discussed.

•Oct 16, 2020•0 citations

Implementation of a two-stroke quantum heat engine with a collisional model

Filipe V. Melo, Nahum Sá, I. Roditi +4 more

We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBM quantum (IBMQ) processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm. The dynamics alternates between heat and work strokes, which can be separately designed using independent quantum circuits. The results show good agreement with theoretical predictions, showcasing IBMQ as a powerful tool to study thermodynamics in the quantum regime, as well as the implementation of variational quantum algorithms in real-world quantum computers. It also opens the possibility of simulating quantum heat transport across a broad range of chain geometries and interactions.

arXiv:2203.13773•Physical Review A•Sep 7, 2022•0 citations

Improving performance of quantum heat engines using modified Otto cycle

B S Revathy, Harsh Sharma, Uma Divakaran

Abstract The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.

arXiv:2302.07003•Journal of Physics A Mathematical and Theoretical•Mar 28, 2024•4 citations

Quantum Stirling heat engine operating in finite time

Debmalya Das, GEORGE M. THOMAS, Andrew N. Jordan

In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that the maximum output power, for the strokes that affect the energy levels, is obtained at an intermediate operating speed, demonstrating the importance of a finite-time analysis.

arXiv:2307.13062•Physical Review A•Jul 28, 2023•12 citations

The multilevel four-stroke swap engine and its environment

Raam Uzdin, Ronnie Kosloff

A multilevel four-stroke engine where the thermalization strokes are generated by unitary collisions with thermal bath particles is analyzed. Our model is solvable even when the engine operates far from thermal equilibrium and in the strong system–bath coupling. Necessary operation conditions for the heat machine to perform as an engine or a refrigerator are derived. We relate the work and efficiency of the device to local and non-local statistical properties of the baths (purity, index of coincidence, etc) and put upper bounds on these quantities. Finally, in the ultra-hot regime, we analytically optimize the work and find a striking similarity to results obtained for efficiency at maximal power of classical engines. The complete swap limit of our results holds for any four-stroke quantum Otto engine that is coupled to the baths for periods that are significantly longer than the thermal relaxation time.

arXiv:1404.6182•New Journal of Physics•Sep 12, 2014•64 citations

Thermodynamical analysis of a quantum heat engine based on harmonic oscillators

Andrea Roberto Insinga, Bjarne Andresen, Peter Salamon

Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

Physical review. E•Jul 15, 2016•51 citations
The formulation of models describing quantum versions of heat engines plays an important role in the quest toward establishing the laws of thermodynamics in the quantum regime. Of particular importance is the description of stroke-based engines, which can operate at finite time. In this paper we put forth a framework for describing stroboscopic, two-stroke engines, in generic quantum chains. The framework is a generalization of the so-called SWAP engine and is based on a collisional model, which alternates between pure heat and pure work strokes. The transient evolution towards a limit cycle is also fully accounted for. Moreover, we show that once the limit cycle has been reached, the energy of the internal sites of the chain no longer changes, with the heat currents being associated exclusively to the boundary sites. Using a combination of analytical and numerical methods, we show that this type of engine offers multiple ways of optimizing the output power, without affecting the efficiency. Finally, we also show that there exists an entire class of models, characterized by a specific type of interchain interaction, which always operate at Otto efficiency, irrespective of the operating conditions of the reservoirs.
In the last decade, the study of thermodynamic phenomena in ultra-small scales, where quantum mechanics becomes imperative, has gained a lot of attention. The possibility of controlling single quantum states in nowadays experimental setups has encouraged a more intense inquiry over the intersection between thermodynamics and quantum mechanics, which is known as quantum thermodynamics. Particularly relevant in this framework is the study of quantum heat engines, that is, quantum systems undergoing thermodynamic cycles. Thermodynamic cycles contain all the aspects of thermodynamics, thus its a good testbed for a better comprehension of the thermodynamics of quantum systems. Moreover, modelling quantum heat engines is crucial for the design of future ultra-small engines. Nonetheless, another aspect must be taken into account, finite-time operation. Its very important for the optimization of the output power of the engine. In this dissertation, we present a new model of finite-time quantum heat engines. By making use of collisional models, we construct a model in which a generic quantum chain experiences sequential pure heat and pure work strokes. Dictated by stroboscopic evolution, the engines state goes through a transient regime until the limit-cycle is reached. After the achievement of the limit-cycle, our results indicate that only the boundary sites of the quantum chain are relevant for the heat currents exchanged with the baths. By means of analytical and numerical methods, we present how the model is useful for optimizing the output power of stroke-based quantum heat engines, without decreasing their respective efficiencies. Lastly, we prove that there is a universal efficiency value, the Otto efficiency, for a whole family of models containing a specific kind of internal interactions. For completeness, other methods from the literature which deal with finite-time quantum heat engines are also presented and discussed.
We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBM quantum (IBMQ) processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm. The dynamics alternates between heat and work strokes, which can be separately designed using independent quantum circuits. The results show good agreement with theoretical predictions, showcasing IBMQ as a powerful tool to study thermodynamics in the quantum regime, as well as the implementation of variational quantum algorithms in real-world quantum computers. It also opens the possibility of simulating quantum heat transport across a broad range of chain geometries and interactions.
Abstract The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.
In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that the maximum output power, for the strokes that affect the energy levels, is obtained at an intermediate operating speed, demonstrating the importance of a finite-time analysis.
A multilevel four-stroke engine where the thermalization strokes are generated by unitary collisions with thermal bath particles is analyzed. Our model is solvable even when the engine operates far from thermal equilibrium and in the strong system–bath coupling. Necessary operation conditions for the heat machine to perform as an engine or a refrigerator are derived. We relate the work and efficiency of the device to local and non-local statistical properties of the baths (purity, index of coincidence, etc) and put upper bounds on these quantities. Finally, in the ultra-hot regime, we analytically optimize the work and find a striking similarity to results obtained for efficiency at maximal power of classical engines. The complete swap limit of our results holds for any four-stroke quantum Otto engine that is coupled to the baths for periods that are significantly longer than the thermal relaxation time.
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.