Magnetic Otto Engine for an Electron in a Quantum Dot: Classical and Quantum Approach

Enhanced Efficiency at Maximum Power in a Fock-Darwin Model Quantum Dot Engine

We study the performance of an endoreversible magnetic Otto cycle with a working substance composed of a single quantum dot described using the well-known Fock-Darwin model. We find that tuning the intensity of the parabolic trap (geometrical confinement) impacts the proposed cycle's performance, quantified by the power, work, efficiency, and parameter region where the cycle operates as an engine. We demonstrate that a parameter region exists where the efficiency at maximum output power exceeds the Curzon-Ahlborn efficiency, the efficiency at maximum power achieved by a classical working substance.

Otto Engine for the q-State Clock Model

This present work explores the performance of a thermal–magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the q− state clock model. We obtain all the thermodynamic quantities for the q = 2, 4, 6, and 8 cases in a small lattice size (3×3 with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the q=4 case, while the performance for the Ising model (q=2) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of q presented in this study.

Quantum Heat Engines with Singular Interactions

By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance.

Performance of quantum heat engines under the influence of long-range interactions

We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two types of thermodynamic cycles, namely, the Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of a long-range interacting heat engine can be boosted by the long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle there exists an optimal condition for which the maximum enhancement in work output and efficiency can be achieved simultaneously by the long-range interactions. But, for the Stirling cycle, the condition which can give the maximum enhancement in work output does not lead to the maximum enhancement in efficiency. We also investigate how the parameter regimes under which the engine performance is enhanced by the long-range interactions evolve with a decrease in the range of interactions.

Otto Engine: Classical and Quantum Approach

In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic 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.

Landauer's Principle in a Quantum Szilard Engine without Maxwell's Demon

Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell’s Demon where Landauer’s principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell’s demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer’s principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer’s principle even in quantum Szilard engines without Maxwell’s demon.

Quasistatic and quantum-adiabatic Otto engine for a two-dimensional material: The case of a graphene quantum dot

In this work, we study the performance of a quasistatic and quantum-adiabatic magnetic Otto cycles with a working substance composed of a single graphene quantum dot modeled by the continuum approach with the use of the zigzag boundary condition. Modulating an external or perpendicular magnetic field, in the quasistatic approach, we found a constant behavior in the total work extracted that is not present in the quantum-adiabatic formulation. We find that, in the quasistatic approach, the engine yielded a greater performance in terms of total work extracted and efficiency as compared with its quantum-adiabatic counterpart. In the quasistatic case, this is due to the working substance being in thermal equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic strokes.

Bosons outperform fermions: The thermodynamic advantage of symmetry

We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that the bosonic system displays enhanced performance when compared to two independent single particle engines, while the fermionic system displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.

Dissipative Endoreversible Engine with Given Efficiency

Endoreversible thermodynamics is a finite time thermodynamics ansatz based on the assumption that reversible or equilibrated subsystems of a system interact via reversible or irreversible energy transfers. This gives a framework where irreversibilities and thus entropy production only occur in interactions, while subsystems (engines, for instance) act as reversible. In order to give an opportunity to incorporate dissipative engines with given efficiencies into an endoreversible model, we build a new dissipative engine setup. To do this, in the first step, we introduce a more general interaction type where energy loss not only results from different intensive quantities between the connected subsystems, which has been the standard in endoreversible thermodynamics up to now, but is also caused by an actual loss of the extensive quantity that is transferred via this interaction. On the one hand, this allows the modeling of leakages and friction losses, for instance, which can be represented as leaky particle or torque transfers. On the other hand, we can use it to build an endoreversible engine setup that is suitable to model engines with given efficiencies or efficiency maps and, among other things, gives an expression for their entropy production rates. By way of example, the modeling of an AC motor and its loss fluxes and entropy production rates are shown.

Entropy Exchange and Thermodynamic Properties of the Single Ion Cooling Process

A complete quantum cooling cycle may be a useful platform for studying quantum thermodynamics just as the quantum heat engine does. Entropy change is an important feature which can help us to investigate the thermodynamic properties of the single ion cooling process. Here, we analyze the entropy change of the ion and laser field in the single ion cooling cycle by generalizing the idea in Reference (Phys. Rev. Lett.2015, 114, 043002) to a single ion system. Thermodynamic properties of the single ion cooling process are discussed and it is shown that the Second and Third Laws of Thermodynamics are still strictly held in the quantum cooling process. Our results suggest that quantum cooling cycles are also candidates for the investigation on quantum thermodynamics besides quantum heat engines.