Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics

Scharlau, Jakob; Mueller, Markus P.

doi:10.22331/q-2018-02-22-54

Cited by 51 publications

(65 citation statements)

References 51 publications

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“…In order to investigate the fundamental limits to the performance of QHEs, we adopt a thermodynamic resource theory approach [15,[43][44][45], where all unitaries U on the global system such that M defines a catalytic thermal operation [16] which one can perform on the joint state ColdW. This implies that the cold bath is used as a non-thermal resource, relative to the hot bath.…”

Section: General Setting Of a Heat Enginementioning

confidence: 99%

Surpassing the Carnot efficiency by extracting imperfect work

Woods

Wehner

2017

New J. Phys.

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A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size. Recently, a number of schemes for QHEs have been proposed and analyzed, involving systems such as ion traps, photocells, or optomechanical systems [2][3][4][5][6][7][8][9][10]. Some of these schemes lie outside the usual heat engine setting (see figure 1). For example, instead of using a hot and cold bath, the extended quantum heat engine (EQHE) has access to reservoirs which are not in a thermal state [3,11,12]. In this case, EQHE with high efficiencies (even surpassing h C ) have been proposed and demonstrated. Nevertheless, [13] has pointed out that the second law is, strictly speaking, never violated because one always has to invest extra work in order to create and replenish these non-thermal reservoirs. Nevertheless, the study of using such non-thermal reservoirs can still be of interest, since they potentially may boost other features of the heat engine, such as the rate of extracting work. However, in this manuscript we are focusing on the standard setting of a QHE, in which the baths are thermal, where in classical thermodynamics, it is proven that although CE can be approached, it can never be surpassed [14].Even without additional resources such as those in EQHEs, QHEs are already radically different from classical engines, since energy fluctuations are much more prominent due to the small number of particles involved. The laws of thermodynamics for small quantum systems are more restrictive due to finite-size effects [14][15][16][17][18][19]. It is known that such second laws introduce additional restrictions on the performance of QHEs [14]. Specifically, not all QHEs can even achieve the CE. The maximal achievable efficiency depends not only on the temperatures, but also on the Hamiltonian structure of the baths involved. Furthermore, considering a probabilistic approach towards work extraction, [20] found that the achievement of CE is very unlikely, when considering energy fluctuations in the microregime.Can we design a QHE that operates between genuinely thermal reservoirs and yet achieves a high efficiency 5 ? To answer this, several protocols have been propos...

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Section: General Setting Of a Heat Enginementioning

confidence: 99%

Surpassing the Carnot efficiency by extracting imperfect work

Woods

Wehner

2017

New J. Phys.

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“…The following two results address the problem of cooling a qubit with Hamiltonian H S = ∆ |1 1 |. In Scharlau's result [17] the initial state of the qubit is ρ S = |1 1 |. But despite being pure, it is not trivial to map it to |0 0 |, because only energy-conserving unitaries are allowed in that setup.…”

Section: B Other Resultsmentioning

confidence: 97%

“…[U, H] = 0 finite bath resource catalyst Allahverdyan (2011) [15] finite d B and J B no yes work no Reeb (2014) [16] finite J B no yes work no Scharlau (2016) [17] finite d B and J B yes yes work no Masanes (2017) [8] finite C B (E) and W wc no yes work no Wilming (2017) [7] finite resources yes no non-eq. yes Müller (2017) [18] finite catalyst yes no both yes…”

Section: Limiting Factormentioning

confidence: 99%

Cooling to Absolute Zero: The Unattainability Principle

Freitas

Gallego

Masanes

et al. 2018

Fundamental Theories of Physics

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The unattainability principle (UP) is an operational formulation of the third law of thermodynamics stating the impossibility to bring a system to its ground state in finite time. In this work, several recent derivations of the UP are presented, with a focus on the set of assumptions and allowed sets of operations under which the UP can be formally derived. First, we discuss derivations allowing for arbitrary unitary evolutions as the set of operations. There the aim is to provide fundamental bounds on the minimal achievable temperature, which are applicable with almost full generality. These bounds show that perfect cooling requires an infinite amount of a given resource-worst-case work, heat bath's size and dimensionality or non-equilibrium states among others-which can in turn be argued to imply that an infinite amount of time is required to access those resources. Secondly, we present derivations within a less general set of operations conceived to capture a broad class of currently available experimental settings. In particular, the UP is here derived within a model of linear and driven quantum refrigerators consisting on a network of harmonic oscillators coupled to several reservoirs at different temperatures. arXiv:1911.06377v1 [quant-ph]

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“…In particular, it was shown in [14] that ideal projective measurements are not exactly realisable in practise because they require the preparation of initially pure pointer states (at least in some nontrivial subspace) to satisfy condition (ii). However, the third law of thermodynamics prevents one from reaching the ground-state of any system with finite resources [15,33,34,[39][40][41][42]. Since any other (pure) state necessarily has higher energy than the ground state, the third law thus excludes ideal measurements.…”

Section: Ideal Measurementsmentioning

confidence: 99%

Work estimation and work fluctuations in the presence of non-ideal measurements

et al. 2019

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From the perspective of quantum thermodynamics, realisable measurements cost work and result in measurement devices that are not perfectly correlated with the measured systems. We investigate the consequences for the estimation of work in non-equilibrium processes and for the fundamental structure of the work fluctuations when one assumes that the measurements are non-ideal. We show that obtaining work estimates and their statistical moments at finite work cost implies an imperfection of the estimates themselves: more accurate estimates incur higher costs. Our results provide a qualitative relation between the cost of obtaining information about work and the trustworthiness of this information. Moreover, we show that Jarzynski's equality can be maintained exactly at the expense of a correction that depends only on the system's energy scale, while the more general fluctuation relation due to Crooks no longer holds when the cost of the work estimation procedure is finite. We show that precise links between dissipation and irreversibility can be extended to the non-ideal situation.

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Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics

Cited by 51 publications

References 51 publications

Surpassing the Carnot efficiency by extracting imperfect work

Surpassing the Carnot efficiency by extracting imperfect work

Cooling to Absolute Zero: The Unattainability Principle

Work estimation and work fluctuations in the presence of non-ideal measurements

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