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arXiv 1612.00518cond-mat.stat-mech
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简单两级热机最大功率输出时的效率

Efficiency at the maximum power output for simple two-level heat engine

Sang Hoon Lee, Jaegon Um, Hyunggyu Park

摘要:

我们引入一个简单的两级热机来研究在最大功率输出条件下的效率,这取决于从中提取净功的能级。与效率达到理论最大值的准静态操作卡诺发动机相比,最近对在有限时间内操作的更现实的发动机的研究揭示了其他类型的效率,例如使功率输出最大化的Curzon-Ahlborn效率。我们研究的另一面与我们的热机模型,它包括纯弛豫和净功提取过程的人口差异所造成的不同的过渡率。由于我们模型的性质,时间依赖部分与生成的工作中的其他项完全解耦。我们推导出最佳条件的转换率最大化的发电功率输出,并讨论其含义的一般前提下,现实的热机。特别是,我们的模型的最佳发动机效率是不同的Curzon-Ahlborn效率,虽然他们共享的通用线性和二次系数在近平衡极限。我们进一步证实了我们的结果,采取另一种方法在热,冷水库的熵产生。

英文摘要:

We introduce a simple two-level heat engine to study the efficiency in the condition of the maximum power output, depending on the energy levels from which the net work is extracted. In contrast to the quasi-statically operated Carnot engine whose efficiency reaches the theoretical maximum, recent research on more realistic engines operated in finite time has revealed other classes of efficiency such as the Curzon-Ahlborn efficiency maximizing the power output. We investigate yet another side with our heat engine model, which consists of pure relaxation and net work extraction processes from the population difference caused by different transition rates. Due to the nature of our model, the time-dependent part is completely decoupled from the other terms in the generated work. We derive analytically the optimal condition for transition rates maximizing the generated power output and discuss its implication on general premise of realistic heat engines. In particular, the optimal engine efficiency of our model is different from the Curzon-Ahlborn efficiency, although they share the universal linear and quadratic coefficients at the near-equilibrium limit. We further confirm our results by taking an alternative approach in terms of the entropy production at hot and cold reservoirs.

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