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arXiv:1009.2536

Maximally efficient quantum thermal machines: The basic principles

Sandu Popescu

Published Sep 13, 2010• 3 citations
arXivHTMLPDF

Abstract

Following the result by Skrzypczyk et al., arXiv:1009.0865, that certain self-contained quantum thermal machines can reach Carnot efficiency, we discuss the functioning of self-contained quantum thermal machines and show, in a very general case, that they can reach the Carnot efficiency limit. Most importantly, the full analytical solution for the functioning of the machines is not required; the efficiency can be deduced from a very small number of fundamental and highly intuitive equations which capture the core of the problem.

DOI
10.48550/arxiv.1009.2536

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Following the result by Skrzypczyk et al., arXiv:1009.0865, that certain self-contained quantum thermal machines can reach Carnot efficiency, we discuss the functioning of self-contained quantum thermal machines and show, in a very general case, that they can reach the Carnot efficiency limit. Most importantly, the full analytical solution for the functioning of the machines is not required; the efficiency can be deduced from a very small number of fundamental and highly intuitive equations which capture the core of the problem.
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An implementation of quantum absorption chillers with three qubits has been recently proposed that is ideally able to reach the Carnot performance regime. Here we study the working efficiency of such self-contained refrigerators, adopting a consistent treatment of dissipation effects. We demonstrate that the coefficient of performance at maximum cooling power is upper bounded by 3/4 of the Carnot performance. The result is independent of the details of the system and the equilibrium temperatures of the external baths. We provide design prescriptions that saturate the bound in the limit of a large difference between the operating temperatures. Our study suggests that delocalized dissipation, which must be taken into account for a proper modeling of the machine-baths interaction, is a fundamental source of irreversibility which prevents the refrigerator from approaching the Carnot performance arbitrarily closely in practice. The potential role of quantum correlations in the operation of these machines is also investigated.
We derive a bound on the efficiency of thermal engines that can be sharper than Carnot's limit. It is a function of statistical correlations between the engine internal state and Hamiltonian, can be saturated even in finite-time cycles, and applies to both classical and quantum engines. Specifically, the bound establishes the exact maximal efficiency of engines operating with multiple baths, tightening the upper limit set by Carnot's theorem. Then, we show that an engine made of a quantum dot coupled with fermionic baths can achieve the bound, even when operating beyond the quasistatic regime. The result provides a design principle for realistic energy harvesting machines.
We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.
Continuous particle exchange thermal machines require no time-dependent driving, can be realised in solid-state electronic devices, and miniaturised to nanometre scale. Quantum dots, providing a narrow energy filter and allowing to manipulate particle flow between the hot and cold reservoirs are at the heart of such devices. It has been theoretically shown that by mitigating passive heat flow, Carnot efficiency can be approached arbitrarily closely in a quantum dot heat engine, and experimentally, values of 0.7ηC have been reached. However, for practical applications, other parameters of a thermal machine, such as maximum power, efficiency at maximum power, and noise - stability of the power output or heat extraction - take precedence over maximising efficiency. We explore the effect of internal microscopic dynamics of a quantum dot on these quantities and demonstrate that its performance as a thermal machine depends on few parameters - the overall conductance and three inherent asymmetries of the dynamics. These parameters will act as a guide to engineering the quantum states of the quantum dot, allowing to optimise its performance beyond that of the simplest case of a two-fold spin-degenerate transmission level.