Quantum mechanical Carnot engine

Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, in considering the Jarzynski equality e −βW = e −β∆F , a change in the fluctuations of e −βW may impact on how fast the statistical average of e −βW converges towards the theoretical value e −β∆F , where W is the work, β is the inverse temperature, and ∆F is free energy difference between two equilibrium states. Motivated by our previous study aiming at the suppression of work fluctuations, here we obtain a principle of minimal work fluctuations. In brief, adiabatic processes as treated in quantum and classical adiabatic theorems yield the minimal fluctuations in e −βW . In the quantum domain, if a system initially prepared at thermal equilibrium is subject to a work protocol but isolated from a bath during the time evolution, then a quantum adiabatic process without energy level crossing (or an assisted adiabatic process reaching the same final states as in a conventional adiabatic process) yields the minimal fluctuations in e −βW , where W is the quantum work defined by two energy measurements in the beginning and at the end of the process. In the classical domain where the classical work protocol is realizable by an adiabatic process, then the classical adiabatic process also yields the minimal fluctuations in e −βW . Numerical experiments based on a Landau-Zener process confirm our theory in the quantum domain, and our theory in the classical domain explains our previous numerical findings regarding the suppression of classical work fluctuations [G. Y. Xiao and J. B. Gong, Phys. Rev. E 90, 052132 (2014)].

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“…(15). In the same manner, the ensemble average e −2β W associated with an adiabatic process is found to be…”

Section: Principle Of Minimal Work Fluctuations: Classical Systemsmentioning

confidence: 56%

Principle of minimal work fluctuations

Xiao

Gong

2015

Phys. Rev. E

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“…Eqs. (13), (14) and (15) leads to the time derivative of the first law of thermodynamics [9,16,33,34]:…”

Section: A Energy Balancementioning

confidence: 99%

Quantum four-stroke heat engine: Thermodynamic observables in a model with intrinsic friction

Feldmann¹,

Kosloff²

2003

Phys. Rev. E

239

224

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The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators which is then used to define the state of the system. The relation between the quantum framework and thermodynamical observables is examined. A four stroke heat engine model with a coupled two-level-system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field which defines the two adiabatic branches. Heat is transferred to the working fluid by coupling to hot and cold reservoirs under constant field values.Explicit quantum equation of motion for the relevant observables are derived on all branches. The dynamics on the heat transfer constant field branches is solved in closed form. On the adiabats, a general numerical solution is used and compared with a particular analytic solution. These solutions are combined to construct the cycle of operation. The engine is then analyzed in terms of frequency-entropy and entropy-temperature graphs. The irreversible nature of the engine is the result of finite heat transfer rates and friction-like behavior due to noncommutability of the internal and external Hamiltonian.

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“…The first law of quantum thermodynamics is fully addressed in many works [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and gives us the possibility to explore different quantum cycles and compare them with the classical analogues. To derivate this law simply, consider a Hamiltonian with an explicit dependence of some parameter that we will call µ in a generic form [25].…”

Section: The First Law Of Quantum Thermodynamicsmentioning

confidence: 99%

“…The possibility to create an alternative and efficient nanoscale device, like its macroscopic counterpart, introduces the concept of the quantum engine, which was proposed by Scovil and Schultz-Dubois in the 1950's [1]. The key point here is the quantum nature of the working substance and of course the quantum versions of the laws of thermodynamics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The combination of these two simple facts leads to very interesting studies of well-known macroscopic engines of thermodynamics, such as Carnot, Stirling and Otto, among others [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

Peña¹,

González²,

Núñez³

et al. 2017

Preprint

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Abstract:We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic quantum Otto engine. The scheme of the cycle is composed of two quantum adiabatic processes and two quantum isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

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Quantum mechanical Carnot engine

Cited by 268 publications

References 1 publication

Principle of minimal work fluctuations

Principle of minimal work fluctuations

Quantum four-stroke heat engine: Thermodynamic observables in a model with intrinsic friction

Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

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