论文标题
小型热发动机的波动与最大功率效率之间的关系
Relation between fluctuations and efficiency at maximum power for small heat engines
论文作者
论文摘要
我们研究了一类涵盖各种典型周期的四冲程热发动机，研究工作输出和热输入方差$η^{（2）} $之间的比率。关于$η^{（2）} $上限和下限的最新研究分别基于绝对极限和线性响应制度。我们将这些关系扩展到可内部近似值内的有限时间制度。我们考虑最大功率的比率$η_{\ text {mp}}^{（2）} $，发现Curzon-Ahlborn效率的平方，$η_{\ text {ca}}}^2 $，给出了$ pex {\ fee for for for for for for foref即，$η_{\ text {mp}}}^{（2）} \ simeqη_{\ text {ca}}}^2 $。这类似于Curzon-Ahlborn效率的情况，可以很好地估算各种有限时间的热发动机的最大功率效率。以谐波电位为例，以谐波潜力的过度阻尼的布朗粒子，我们可以意识到这种可逆的小型热发动机，并表达工作输出和热输入的累积物。近似关系$η_ {\ text {mp}}}^{（2）} \ simeqη_ {\ text {ca}}^2 $通过数值模拟验证。这种关系还表明，有限时间的热发动机的效率和稳定性之间的权衡。
We study the ratio between the variances of work output and heat input, $η^{(2)}$, for a class of four-stroke heat engines which covers various typical cycles. Recent studies on the upper and lower bounds of $η^{(2)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio $η_{\text{MP}}^{(2)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, $η_{\text{CA}}^2$, gives a good estimate of $η_{\text{MP}}^{(2)}$ for the class of heat engines considered, i.e., $η_{\text{MP}}^{(2)} \simeq η_{\text{CA}}^2$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation $η_{\text{MP}}^{(2)} \simeq η_{\text{CA}}^2$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.
