Entropy and temperature of a quantum Carnot engine

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.

show abstract

“…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

238

224

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…Since the kinetic theory of Boltzmann gas tells that a moving piston does not play a role in the equation of states, we shall investigate the nonadiabatic dynamics in the quantum heat engine. While in recent years there appeared papers which treated the quantum engine, they were either concerned with a quantum analog of Carnot's engine [4][5][6][7] or with a quantum analog of nonequilibrium work relation (i.e., fluctuation theorem) [8,9]. And no work so far was engaged in nonadiabatic force and pressure due to a moving piston and in the statistical treatment of a noninteracting Fermi gas.…”

Section: Introductionmentioning

confidence: 99%

Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston

et al. 2012

View full text Add to dashboard Cite

We study a nonequilibrium equation of states of an ideal quantum gas confined in the cavity under a moving piston with a small but finite velocity in the case that the cavity wall suddenly begins to move at time origin. Confining to the thermally-isolated process, quantum non-adiabatic (QNA) contribution to Poisson's adiabatic equations and to Bernoulli's formula which bridges the pressure and internal energy is elucidated. We carry out a statistical mean of the non-adiabatic (timereversal-symmetric) force operator found in our preceding paper (K. Nakamura et al, Phys. Rev. E83, 041133 (2011)) in both the low-temperature quantum-mechanical and high temperature quasiclassical regimes. The QNA contribution, which is proportional to square of the piston's velocity and to inverse of the longitudinal size of the cavity, has a coefficient dependent on temperature, gas density and dimensionality of the cavity. The investigation is done for a unidirectionally-expanding 3-d rectangular parallelepiped cavity as well as its 1-d version. Its relevance in a realistic nano-scale heat engine is discussed.

show abstract

Entropy and temperature of a quantum Carnot engine

Cited by 94 publications

References 10 publications

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

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

Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston

Contact Info

Product

Resources

About