Efficiency at Maximum Power Output of a Quantum-Mechanical Brayton Cycle

Abstract

The performance in finite time of a quantum-mechanical Brayton engine cycle is discussed, without introduction of temperature. The engine model consists of two quantum isoenergetic and two quantum isobaric processes, and works with a single particle in a harmonic trap. Directly employing the finite-time thermodynamics, the efficiency at maximum power output is determined. Extending the harmonic trap to a power-law trap, we find that the efficiency at maximum power is independent of any parameter involved in the model, but depends on the confinement of the trapping potential.

Quantum-Mechanical Brayton Engine for the Nonrelativistic Particle Trapped in a Symmetric Potential Box

“…The particle wave function in this stage is Φ ( , , ) = 211 211 + 121 121 + 112 112 . (12) with the system's total energy is ( ) = 6 2 ℏ 2 2 2 (13) By knowing the system's total energy in this process contained in the equation ( 13), the mechanical force of the wall in this process is…”

“…Then, this classical system is substituted by a quantum system. The quantum system applied can be either an infinite potential well [3][4][5][6][7][8][9][10][11] or a harmonic oscillator [12][13][14] to produce an engine efficiency that exceeds the classical version.…”

Universal Expression of Efficiency at Maximum Power: A Quantum-Mechanical Brayton Engine Working with a Single Particle Confined in a Power-Law Trap

“…If the confining potential is a harmonic trap, where θ = 2 and σ = 1, the efficiency at maximum power for the engine working between two pure states was proved to be 0.452 036. [15] By contrast, the efficiency at maximum power is enhanced by involving superposition of quantum states, and it approaches its maximum value, η * = 2/3, when G tends to be infinity (see more details in Table 1).…”

Local stability analysis of a low-dissipation cyclic refrigerator *

“…The optimal analysis on finite-time performance of thermal machines that include heat engines and refrigerators has attracted much interest , beginning with the seminar work [1]. Among these, the low-dissipation model [12][13][14][15][16][17][18][19][20][21][22][23][24][25] in which the thermal-contact process is not quasi-static but close to the reversible limit was usually adopted, with the advantage that neither phenomenological heat-transfer laws nor quantum master equations are used. Under the low-dissipation assumption, the irreversible entropy production along a thermal-contact process is inversely proportional to the longtime duration t. Such a 1/t − scaling entropy production was theoretically proved in classical [26,27] and quantum systems [28,29], and it was also validated in recent experiments [30,31] based on different platforms.…”