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研究生:張朝昇
研究生(外文):Chang, Chao-Sheng
論文名稱:離子幫浦的隨機熱力學
論文名稱(外文):Stochastic Thermodynamics in Ion Pumps
指導教授:張正宏張正宏引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:54
中文關鍵詞:隨機熱力學
外文關鍵詞:Stochastic ThermodynamicsIntegral Fluctuation Theorem (IFT)Detailed Fluctuation Theorem (DFT)
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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.

誌謝 II
Abstract III
摘要 IV
Content 1
1 Stochastic thermodynamics 1
1.1 Integral fluctuation theorem and detailed fluctuation theorem 2
The detailed balance condition and the static detailed balance condition 3
The derivation of the IFT for a master equation 3
1.2 Stochastic entropy along a single trajectory 7
2 An experiment test and simulation for two-state system 12
2.1 Experimental test for entropy production of a two-level system 12
2.2 Reproduction of the experiment by simulation 14
2.3 Improvements in simulation 20
2.3.1 Consideration of the ensemble average of states 20
2.3.2 Estimation for quantity of statistics 24
2.4 Brief conclusion 31
3 A simulation for entropy production for four-state system 32
3.1 The four-state system for ion pumps 32
3.2 The simulation for four-state system 32
3.2.1 Time-dependent detailed balance condition without net flow 33
3.2.2 Static detailed balance condition with net flow 35
3.2.3 Non-detailed balance condition without time-dependent driving 39
3.2.4 Non-detailed balance condition with time-dependent driving 42
3.3 Brief conclusion 49
Conclusions and Future Works 51
Reference 53

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[10] E.H. Serpersu, T.Y. Tsong, J. Biol. Chem. 259 (1984) 7155.
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[12] A. Fulinski, Phys. Rev. Lett. 79, 4926 (1997); Chaos 8, 549(1998); A. Fulinski and P.F. Go´ra, Phys. Rev. E 64, 011905(2001).

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