Stochastic thermodynamics of colloidal heat engines

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艾約翰(John Andrew C. Albay) 查詢紙本館藏

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物理學系

論文名稱

(Stochastic thermodynamics of colloidal heat engines)

相關論文

★ 等溫過程中平衡捷徑之實驗研究	★ 蜂擁菌群中被動粒子統計特性之實驗研究
★ 布朗粒子的自發性熱機	★ 研究在擁擠環境中由多個驅動蛋白拖曳的貨物速度

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摘要(中)

熱機的發展和熱力學的研究在 19 世紀齊頭並進。卡諾對理想熱機的研究已成為測量其他熱機效率的基準。在過去的二十年裡，由於微型化技術以及理解隨機系統理論的進步，``微觀′′熱機的熱力學引起了更多的關注。在相關的主題中，我們專注於提高熱機的性能，例如效率和功率。

此論文涵蓋三個部分：i）如何架設具有回饋控制的光鑷系統，ii）展示膠體布朗粒子運動的熱機，以及iii）對於在有限時間內瞬間抵達平衡態的研究。

為了能夠控制單一布朗粒子的擾動，我們開發了一種能夠操縱位能和調節溫度的裝置。具有探測精準位置以及超快速回饋控制的光鑷(OFT)，可以產生客製形狀且與時相關的位能，並能精確控制等效溫度。OFT 創建了一個虛擬系統來模擬布朗運動的粒子被限制在真實溫度下的現實位能內 [Albay et al., Opt. Exp. (2018), Albay et al., Sci. Rep. (2021)]。為了展示 OFT 研究熱力學問題的便利性，我們研究布朗粒子的非平衡動力學，該粒子被限制在剛度線性變化的諧位能中，並驗證了 Crooks 的漲落定理 [Albay et al., Opt. Exp. (2018)]。

憑藉 OFT 的優勢，最明顯的應用是熱機的演示。我們實現了一個微型史特林熱機，該熱機由一個布朗粒子組成，該粒子受到時變諧位能的限制並可以週期性地控制溫度。該熱機的效率可以在準靜態極限處達到熱力學極限，並顯示其在效率和功率之間的權衡關係 [Albay et al., Sci. Rep. (2018)]。此外，相較於熱浴中的熱機，細菌浴接觸的熱機較其效率高且以此聞名，但其原因不明。我們採用 Ornstein-Ulehnbeck 噪聲來模擬細菌對粒子擾動的影響，並顯示效率可以藉著調整對於給定噪聲關聯時間的噪聲大小而改變，則發動機的效率可以在準靜態極限超過被動熱浴發動機的效率 [Albay et al., Submitted (2022)]。

對於發動機的這兩種情況，功率在最大效率下都可以忽略不計。下一個挑戰是開發一種在最大效率下具有有限功率的發動機。為了實現有限速率轉變，我們通過對控制參數施加適當的約束來實現保持瞬時平衡的等溫過程捷徑。我們考慮三種不同的情況：第一種是布朗粒子被諧位能移動到不同的位置，第二種是改變諧位能的剛度，第三種是改變非和諧位能的剛度。我們確認在轉變後系統立即達到平衡狀態，並發現在所有三種情況下耗散功都與驅動時間成反比，這表明瞬時轉變是不可能的 [Albay et al., Phys. Rev. Res. (2019), Albay et al., Appl. Phys. Lett. (2020)]。最後，我們確立出一個新的作功關係式，即正向過程中瞬時轉變的耗散功與相應的逆向過程相同 [Albay et al., New J. Phys. (2020)]。

摘要(英)

The development of heat engines and the study of thermodynamics went hand in hand in the 19th century.
Carnot′s study of an ideal engine has served as a benchmark for measuring the efficiency of other heat engines.
Over the past two decades, the thermodynamics of ``microscopic′′ heat engines has attracted more attention due to technological advances in miniaturization and theoretical advancements in understanding stochastic systems.
Among other relevant topics, we focus on enhancing the performance of heat engines, such as efficiency and power.

This thesis consists of three parts: i) the development of the optical feedback trap, ii) the demonstration of colloidal heat engines, and iii) the study of the instantaneous equilibrium transition in finite time.

To control the fluctuation of a single Brownian particle, we develop a device capable of manipulating potentials and regulating temperature.
The optical feedback trap (OFT), which is based on precise position detection and ultrafast feedback control, can create a time-dependent potential with any desired shape and precisely control the effective temperature.
The OFT creates a virtual system that mimics the environment of a Brownian particle confined in a real potential at a real temperature [Albay et al., Opt. Exp. (2018), Albay et al., Sci. Rep. (2021)].

To display the ease of the OFT to study thermodynamic problems, we study the nonequilibrium dynamics of a Brownian particle confined in a harmonic potential where the stiffness varies linearly and verify the Crooks fluctuation theorem [Albay et al., Opt. Exp. (2018)].

With the advantages of the OFT, the most apparent application is the demonstration of heat engines.
We realize a microscopic Stirling heat engine consisting of a Brownian particle confined by a time-varying harmonic potential and periodically controlling temperature.
The engine′s efficiency can reach the thermodynamic bound of efficiency at the quasistatic limit and displays the trade-off relation between its efficiency and power [Albay et al., Sci. Rep. (2018)].

Moreover, the heat engine in contact with the bacterial bath is known for the higher efficiency than the engine efficiency in the thermal bath, but its origin is unknown.
We adopt the Ornstein-Ulehnbeck noise to mimic the bacterial effect on a particle′s fluctuation and show that the efficiency can be modulated by tuning the strength of noise at the given correlation time of noise.
If the noise level is tuned according to the harmonic potential′s stiffness, the engine′s efficiency can surpass that of a passive bath heat engine in the quasistatic limit [Albay et al., Submitted (2022)].

For both cases of the engine, power is negligible at the maximum efficiency.
The next challenge is developing an engine having finite power at maximum efficiency.
To achieve a finite-rate transition, we implement the shortcut-to-isothermality protocol to maintain instantaneous equilibrium by imposing the appropriate constraints on the control parameter.
We consider three different cases: the first is a Brownian particle dragged to a different position by a harmonic potential, the second is the change in stiffness of the harmonic potential, and the third is the change in stiffness of a nonharmonic potential.
We confirm that the equilibrium state is achieved immediately after transition and found that the dissipated work is inversely proportional to the driving time in all three cases, indicating that an instantaneous transition is impossible [Albay et al., Phys. Rev. Res. (2019), Albay et al., Appl. Phys. Lett. (2020)].

Finally, we confirm a new work relation stating that the dissipated work of the instantaneous transition of the forward process is identical to that of the corresponding reverse process [Albay et al., New J. Phys. (2020)].

關鍵字(中)

★ 隨機熱力學
★ 熱機
★ 膠體
★ 反饋陷阱

關鍵字(英)

★ Stochastic Thermodynamics
★ Heat engine
★ Colloid
★ Feedback trap

論文目次

摘要.........ix
Abstract.........xi
Acknowledgements.........xiii
1 Introduction.........1
1.1 Why Stochastic heat engine?.........1
2 Stochastic Thermodynamics.........7
2.1 Classical thermodynamics to Stochastic thermodynamics.........7
2.2 Langevin equation.........9
2.3 Stochastic calculus.........13
2.4 Sekimoto’s approach.........14
2.4.1 Work and heat in microscopic scale.........14
2.5 Entropy in stochastic system.........16
2.6 Fluctuation Theorem.........16
2.6.1 Crook’s fluctuation theorem.........17
2.6.2 Jarzynski relation.........18
3 Optical tweezers.........19
3.1 Optical trapping regime.........20
3.1.1 Ray optics regime: r ≫ λ.........20
3.1.2 Rayleigh regime: r ≪ λ.........22
3.1.3 Ray scattering regime: r ∼ λ.........22
3.2 Designing the Optical tweezers.........23
3.2.1 Laser.........23
3.2.2 Microscope.........24
3.2.3 Position control.........25
3.2.4 Position detection.........26
3.2.5 Acquisition hardware.........27
3.3 Building of optical tweezers.........28
3.4 Calibration of Optical tweezers.........31
3.4.1 Determination of conversion factors.........31
3.4.1.1 Camera Image.........31
3.4.1.2 AOD calibration.........32
3.4.2 Stiffness calibration.........33
3.4.2.1 Power spectrum analysis.........33
3.4.2.2 Equipartition theorem.........34
4 Optical Feedback trap.........37
4.1 Concept of Feedback.........37
4.2 Generation of virtual potential.........39
4.2.1 Breathing potential experiment.........42
4.2.2 Double well potential.........44
4.3 Generation of virtual Temperature.........46
5 Heat engine in colloidal system.........51
5.1 Thermodynamic processes.........52
5.1.1 Iso-temperature process.........52
5.1.2 Iso-stiffness process.........53
5.2 A microscopic Stirling engine.........55
6 Active bath heat engine.........65
6.1 Creation of correlated noise.........66
6.2 OU noise as non-equilibrium temperature.........67
6.3 Constant Tou active bath heat engine.........67
6.4 Comparison of Active bath heat engine and Passive bath heat engine.........70
7 Instantaneous equilibrium process.........77
7.1 Shortcut to Isothermality (ScI).........78
7.2 Experimental validation of ScI.........79
7.2.1 Brownian harmonic transport.........80
7.2.2 Time-varying harmonic potential (HP).........84
7.2.3 Time-varying non-harmonic potential (NHP).........86
7.3 Derivation of the Work Relation for the ScI processes: ⟨W⟩ = ⟨WR⟩ + 2∆F.........89
8 Conclusion.........93
A Lens basics.........95
B Distributions of thermodnamic quantities in long time limit.........99
Bibliography .........101

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指導教授

田溶根(Yonggun Jun)

審核日期

2022-7-25

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