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arXiv:1910.04734 · Physical review. E

Bosons outperform fermions: The thermodynamic advantage of symmetry

Nathan M. Myers, Sebastian Deffner

Published Jan 8, 2020• 66 citations
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Abstract

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.

DOI
10.1103/physreve.101.012110

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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.
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.
Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.
We study a minimal quantum Otto heat engine, where the working medium consists of an interacting few-body system in a harmonic trap. This allows us to consider the interaction strength as an additional tunable parameter during the work strokes. We calculate the figures of merit of this engine as a function of the temperature and show clearly in which parameter regimes the interactions assist in engine performance. We also study the finite-time dynamics and the subsequent tradeoff between the efficiency and the power, comparing the interaction-enhanced cycle with the case where the system remains scale-invariant.
At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose-Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power.
We present a detailed study of an asymmetrically driven quantum Otto engine with a time-dependent harmonic oscillator as its working medium. We obtain analytic expressions for the upper bounds on the efficiency of the engine for two different driving schemes having asymmetry in the expansion and compression work strokes. We show that the Otto cycle under consideration cannot operate as a heat engine in the low-temperature regime. Then, we show that the friction in the expansion stroke is significantly more detrimental to the performance of the engine as compared to the friction in the compression stroke. Further, by comparing the performance of the engine with sudden expansion, sudden compression, and both sudden strokes, we uncover a pattern of connections between the operational points, and we indicate the optimal operation regime for each case. Finally, we analytically characterize the complete phase diagram of the Otto cycle for both driving schemes and highlight the different operational modes of the cycle as a heat engine, refrigerator, accelerator, and heater.
We investigate a quantum Otto engine with a quantum Ising spin glass as the working medium to explore the scaling behavior of work output and thermodynamic performance concerning system size, particularly near the critical point. Specifically, we explore the two operating modes of the Otto engine, namely the heat engine and refrigerator modes. We observe a double-peaked structure in the heat engine regime, leading to superlinear scaling in both work output and thermodynamic performance near the critical point. Additionally, in the refrigerator regime, superlinear scaling in refrigerator efficiency can be achieved at high and low temperatures, significantly outperforming models with uniform Ising interactions. These findings suggest that disorder and frustration in quantum Ising spin-glass systems could significantly impact thermodynamic performance in quantum heat engines and refrigerators, potentially opening up new avenues for improvement.