離子幫浦的隨機熱力學

Abstract

這篇論文共分為三章。 在第一章，我們為隨機熱力學(Stochastic Thermodynamics)做簡短的介紹，並利用時間反轉的方法證明離散系統(discrete system)中的Integral Fluctuation Theorem (IFT)。IFT原本只是數學上的結果，但如果我們引進單一路徑的entropy定義 [1]，我們就可以得到隨機熱力學中的IFT。 在第二章，我們介紹一個二階系統的實驗 [2]，這是一個在鑽石中受週期雷射激發的單一缺陷。一個缺陷會有基態和激發態兩種狀態，而對於很多個缺陷則可以用master equation來描述它們所處狀態的濃度。透過這個實驗，可以檢驗二階系統中單一路徑的entropy定義、IFT，以及Detailed Fluctuation Theorem (DFT) 的正確性。接著我們用程式模擬這個二階系統和實驗結果，並進一步地改善實驗條件，使得結果更接近IFT和DFT的理論值。 在第三章，我們討論各種不同條件下的鈉鉀離子幫浦的隨機熱力學，像是外加不同的外場，以及系統是不是符合detailed balance condition. 我們先將其簡化成四階系統，並應用第二章的模擬方法去討論各種條件下的情形。

This thesis consists of three chapters. In chapter 1, we give a brief introduction to stochastic thermodynamics, and then make use of the notion of time-reversal to derive the integral fluctuation theorem (IFT) as a mathematical result for general discrete-state system governed by a master equation. Next, applying the definition [1] of entropy along a single stochastic trajectory, we get the integral fluctuation theorem (IFT) for stochastic thermodynamics. In chapter 2, we first sketch the two-level experiment with a single defect center in diamond periodically excited by a laser [2], which verified the validity of the definition of entropy along a stochastic trajectory, as well as integral fluctuation theorem (IFT) and detailed fluctuation theorems (DFT) in a two-state system. Then, we develop a simulation for the Markovian process in this discrete system, to confirm the experimental observation. Next, we improve the experimental conditions in the simulation and get more information than the experiments about how the data collected converge to the IFT and DFT. In chapter 3, we apply the similar simulation to the four-state system of ion pumps and discuss stochastic thermodynamics under different conditions, such as different external protocols and whether obey detailed balance condition.