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

Origin of the quantum shape effect

The quantum size and shape effects are often considered difficult to distinguish from each other because of their coexistence. Essentially, it is possible to separate them and focus solely on the shape effect by considering a size-invariant shape transformation, which changes the discrete energy spectra of strongly confined systems and causes the quantum shape effects. The size-invariant shape transformation is a geometric technique of transforming shapes by preserving the boundary curvature, topology, and the Lebesgue measure of a bounded domain. The quantum shape effect is a quite different phenomenon from quantum size effects, as it can have the opposite influence on the physical properties of nanoscale systems. While quantum size effects can usually be obtained via bounded continuum approximation, the quantum shape effect is a direct consequence of the energy quantization in specifically designed confined geometries. Here, we explore the origin of the quantum shape effect by theoretically investigating the simplest system that can produce the same physics: quantum particles in a one-dimensional box separated by a moving partition. The partition moves quasistatically from one end of the box to the other, allowing the system to remain in equilibrium with a reservoir throughout the process. The partition and the boundaries are impenetrable by particles, forming two effectively interconnected regions. The position of the partition becomes the shape variable. We investigate the quantum shape effect on the thermodynamic properties of confined particles considering their discrete spectrum. In addition, we applied an analytical model based on dimensional transitions to predict thermodynamic properties under the quantum shape effect accurately. A fundamental understanding of quantum shape effects could pave the way for employing them to engineer physical properties and design better materials at the nanoscale.

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 Complex Working Media, Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.

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.

Quantum Photovoltaic Cells Driven by Photon Pulses

We investigate the quantum thermodynamics of two quantum systems, a two-level system and a four-level quantum photocell, each driven by photon pulses as a quantum heat engine. We set these systems to be in thermal contact only with a cold reservoir while the heat (energy) source, conventionally given from a hot thermal reservoir, is supplied by a sequence of photon pulses. The dynamics of each system is governed by a coherent interaction due to photon pulses in terms of the Jaynes-Cummings Hamiltonian together with the system-bath interaction described by the Lindblad master equation. We calculate the thermodynamic quantities for the two-level system and the quantum photocell including the change in system energy, the power delivered by photon pulses, the power output to an external load, the heat dissipated to a cold bath, and the entropy production. We thereby demonstrate how a quantum photocell in the cold bath can operate as a continuum quantum heat engine with a sequence of photon pulses continuously applied. We specifically introduce the power efficiency of the quantum photocell in terms of the ratio of output power delivered to an external load with current and voltage to the input power delivered by the photon pulse. Our study indicates a possibility that a quantum system driven by external fields can act as an efficient quantum heat engine under non-equilibrium thermodynamics.