Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

Ng, Nelly Huei Ying; Woods, Mischa P.

doi:10.1007/978-3-319-99046-0_26

Cited by 36 publications

(62 citation statements)

References 84 publications

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“…The optimal way to achieve this remains an open question. See [43] for partial results and Section V in [4] for a more in-depth discussion. The initial state of our heat engine will be of the form…”

Section: Setup 21 the Heat Engine Modelmentioning

confidence: 99%

“…Unlike the large scale heat engines that inspired thermodynamics, we are now able to build nanoscale quantum machines consisting of a mere handful of particles, and this has prompted many efforts to understand quantum thermodynamics [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. In particular, given such nanoscale devices, one of the main issues addressed in quantum thermodynamics is the single-shot analysis of thermodynamical state transitions or work extraction.…”

Section: Introductionmentioning

confidence: 99%

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The maximum efficiency of nano heat engines depends on more than temperature

Woods

Wehner

2019

Quantum

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Sadi Carnot's theorem regarding the maximum efficiency of heat engines is considered to be of fundamental importance in thermodynamics. This theorem famously states that the maximum efficiency depends only on the temperature of the heat baths used by the engine, but not on the specific structure of baths. Here, we show that when the heat baths are finite in size, and when the engine operates in the quantum nanoregime, a revision to this statement is required. We show that one may still achieve the Carnot efficiency, when certain conditions on the bath structure are satisfied; however if that is not the case, then the maximum achievable efficiency can reduce to a value which is strictly less than Carnot. We derive the maximum efficiency for the case when one of the baths is composed of qubits. Furthermore, we show that the maximum efficiency is determined by either the standard second law of thermodynamics, analogously to the macroscopic case, or by the non increase of the max relative entropy, which is a quantity previously associated with the single shot regime in many quantum protocols. This relative entropic quantity emerges as a consequence of additional constraints, called generalized free energies, that govern thermodynamical transitions in the nanoregime. Our findings imply that in order to maximize efficiency, further considerations in choosing bath Hamiltonians should be made, when explicitly constructing quantum heat engines in the future. This understanding of thermodynamics has implications for nanoscale engineering aiming to construct small thermal machines.

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Section: Setup 21 the Heat Engine Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The maximum efficiency of nano heat engines depends on more than temperature

Woods

Wehner

2019

Quantum

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“…Resource theories thus provide a set of criteria for determining whether a proposed quantity counts as a valid measure of the resource. They have been instrumental in understanding quantum reference frames [30], thermodynamics [31][32][33][34], coherence [35][36][37], contextuality [38], steering [39], and non-Gaussianity [40][41][42][43]. Resourcetheoretic terminology in continuous variables has appeared in a number of recent works [44][45][46][47][48][49][50][51][52], but these ideas are still in their infancy.…”

Section: Introductionmentioning

confidence: 99%

Operational Resource Theory of Continuous-Variable Nonclassicality

et al. 2018

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Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P-representation -a state lacking a positive P-function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed-forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multi-mode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single mode Gaussian states.

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“…There are several approaches to this, depending on which operations are considered to be the free operations of the resource theory. The most widespread approach relies on thermal operations [1][2][3], which are reviewed in [4]. Instead, we consider adiabatic processes here, which are central to Lieb and Yngvason's axiomatic approach to phenomenological thermodynamics [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Smooth Entropy in Axiomatic Thermodynamics

Weilenmann

Gabriel

Faist

et al. 2018

Fundamental Theories of Physics

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Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including microscopic systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. arXiv:1807.07583v1 [quant-ph]

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Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

Cited by 36 publications

References 84 publications

The maximum efficiency of nano heat engines depends on more than temperature

The maximum efficiency of nano heat engines depends on more than temperature

Operational Resource Theory of Continuous-Variable Nonclassicality

Smooth Entropy in Axiomatic Thermodynamics

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