Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511, Luxembourg, Luxembourg.
Theoretical physics, Hasselt University, B-3590, Diepenbeek, Belgium.
Nat Commun. 2014 Sep 15;5:4721. doi: 10.1038/ncomms5721.
The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit. Furthermore, the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on two model systems.
传统上，热机的效率被定义为其平均输出功与平均输入热之比。它的最高可能值是由卡诺在 1824 年发现的，是热力学中的一个基石概念。它导致了第二定律的发现，并定义了开尔文温度标度。小尺度发动机在输入和输出能量通量高度波动的情况下运行。因此，它们的波动性效率特征要好得多。在这项研究中，我们使用涨落定理来确定效率波动的普遍特征。虽然标准热力学效率是最有可能的值，如预期的那样，但我们发现，在长时间限制下，令人惊讶的是，卡诺效率是最不可能的。此外，当接近平衡时，效率的概率分布呈现出普遍的标度形式。我们在两个模型系统上进行了分析和数值说明。
