高效率微觀Stirling熱機的起因

近年來，對微觀熱機上有許多理論研究與實驗，除了由高斯白噪聲驅動的布朗卡諾引擎外，最引人注意的一種是由細菌驅動的主動Stirling引擎。這種主動Stirling引擎的效率高於傳統熱力學中已知的宏觀Stirling引擎的上界效率。它啟發了數個熱力學問題，包含噪聲的何種屬性是至關產生高效率的因素，及是否可能超過卡諾效率的上限。在本文中，我們徹底研究了在描述微觀引擎的Langevin方程中的三個項。我們的分析不僅排除了幾個先前所知高斯色噪聲與非高斯噪聲產生高效率的可能，並且發現了一些特殊形式的噪聲得以超出傳統效率的極限。不僅如此，本研究深入地探討記憶效應於位能項中發生的高效率且降低了速度項中耗散核的重要性。此外，我們討論了檢查高效能引擎及其關係的不同標準。該研究對觀察到的微觀Stirling引擎高性能的可能機制提供了更為清晰的見解，並且可能會加速在小世界中實驗上對高效機器的探究。

關鍵字

效率；微觀Stirling 熱機；噪聲

並列摘要

Recently, there have been many theoretical and experimental studies on the microscopic heat engines. In addition to the Brownian Carnot engine driven by the Gaussian white noises, the most fascinating one is an active Stirling engine driven by bacteria. Such kind of active Stirling engine shows an efficiency higher than the traditional limit set by the macroscopic Stirling engines. It inspires several thermodynamic questions, including the crucial noise properties for the high efficiency and the possibility of exceeding the Carnot efficiency. In this thesis, we thoroughly investigated the three terms in the Langevin equation describing the microscopic engines. Our analysis excluded several previously known colored and non-Gaussian noises for high efficiency, but also discovered some specific noise types which override the traditional efficiency limit. Furthermore, the study highlighted the essence of the memory effect in the potential term for the high efficiency and degrades the importance of the dissipation kernel in the velocity term. Additionally, we discussed different criteria for examining high efficiency engines and their relations. The study gives a much clearer insight into possible mechanisms for the observed high performance of the microscopic Stirling engines and may accelerate the experimental search of efficient machines in the small world.