Performance of a multilevel quantum heat engine of an idealN-particle Fermi system

Abstract

We generalize the quantum heat engine (QHE) model which was first proposed by Bender et al. [J. Phys. A 33, 4427 (2000)] to the case in which an ideal Fermi gas with an arbitrary number N of particles in a box trap is used as the working substance. Besides two quantum adiabatic processes, the engine model contains two isoenergetic processes, during which the particles are coupled to energy baths at a high constant energy E(h) and a low constant energy E(c), respectively. Directly employing the finite-time thermodynamics, we find that the power output is enhanced by increasing particle number N (or decreasing minimum trap size L(A)) for given L(A) (or N), without reduction in the efficiency. By use of global optimization, the efficiency at possible maximum power output (EPMP) is found to be universal and independent of any parameter contained in the engine model. For an engine model with any particle-number N, the efficiency at maximum power output (EMP) can be determined under the condition that it should be closest to the EPMP. Moreover, we extend the heat engine to a more general multilevel engine model with an arbitrary 1D power-law potential. Comparison between our engine model and the Carnot cycle shows that, under the same conditions, the efficiency η = 1 - E(c)/E(h) of the engine cycle is bounded from above the Carnot value η(c) =1 - T(c)/T(h).

Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation

“…The influence on the performance of a classical or quantum heat engine, induced by internally dissipative dissipation (such as inner friction and internal dynamics, etc. ), has been discussed in several papers [28][29][30][31][32][33][34][35]. To the best of our knowledge, so far little attention has been paid to the effects of nonadiabatic dissipation on the performance characteristics of the refrigerators proceeding with finite time.…”

Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

“…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].…”

“…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].…”

Magnetic Engine for the Single-Particle Landau Problem

“…The last equation corresponds to the microscopic formulation of the first law of thermodynamics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][25][26][27]31,34,35]. The first term in Equation (10) is associated with the energy exchange, while the second term represents the work done.…”

“…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 1950s [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].…”