Abstract

We consider the toy model of quantum Diesel cycle without temperature constructed from non-interacting fermions, which are trapped in a one-dimensional box. The work and energy extracted from the cycle are by changing the expectation value of Hamiltonian. We analytically calculated the efficiency of the cycle and efficiency at maximum work as a function of compression ratio. We found that the efficiency of the engine depends on both compression ratio and cut-off ratio. In contrast, the efficiency at the maximum work can be written as a function of the compression ratio only. Moreover, we calculate the Clausius relation of the cycle. The degree of the irreversibility of the cycle depends only on the cut-off ratio. We also study the relation between power and efficiency of the cycle. The power output is also studied as the function of the compression ratio. It is found that for a given value of the cutoff ratio, the dimensionless power output decreases as the compression ratio increases.

Graphical abstract

中文翻译：

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一维盒子中非相互作用费米子的多级量子柴油机

摘要

我们考虑由非相互作用的费米子构成的无温度的量子柴油循环玩具模型，费米子被困在一维盒子中。从循环中提取的功和能量是通过更改哈密顿量的期望值来实现的。我们分析计算出循环效率和最大工作效率与压缩比的关系。我们发现发动机的效率取决于压缩比和截止比。相反，最大功的效率只能写成压缩比的函数。此外，我们计算周期的克劳修斯关系。循环的不可逆程度仅取决于截止率。我们还研究了功率与循环效率之间的关系。还研究了功率输出与压缩比的关系。发现对于给定的截止比值，无因次功率输出随着压缩比的增加而降低。

图形概要