Title Page

Abstract

Contents

Chapter 1. Introduction 15

1.1. Brownian motion 18

1.1.1. Langevin equation 19

1.2. Stochastic thermodynamics 21

1.2.1. Equilibrium Langevin system 21

1.2.2. Nonequilibrium Langevin system 23

1.2.3. Fluctuation theorem 24

1.3. Fluctuation relation for heat 29

Reference 32

Chapter 2. Brownian information engine 36

2.1. Introduction 36

2.2. Brownian information engine model 39

2.3. Fixed potential-center dynamics 43

2.4. Optimal tuning of the engine 46

2.4.1. τ → ∞ case 47

2.4.2. τ → 0 case 48

2.4.3. Finite τ case 52

2.5. Conclusion 60

Reference 62

Chapter 3. Brownian heat engine 67

3.1. Introduction 67

3.2. Brownian heat engine model 69

3.3. Efficiency of the engine 71

3.4. Large deviation function for the efficiency 73

3.5. Conclusion 84

Reference 87

Chapter 4. Ising model on a rewiring network 90

4.1. Nonequilibrium Ising model 90

4.2. Ising spins on an annealed network 93

4.2.1. q-neighbor Ising model 93

4.2.2. Nonequilibrium Ising model on an active network 95

4.3. Mean field theory 97

4.4. Phase diagram 101

4.4.1. Equilibrium case with TS＝TL＝Teq(이미지참조) 107

4.4.2. Tricritical point 110

4.5. Summary and discussions 113

Reference 117

Chapter 5. Summary 120

Reference 124

Bibliography 125

Abstract in Korean 138

Table 4.1. Quartet configurations with sx＝+ and associated energy costs and...(이미지참조) 98

Figure 2.1. Illustration of the engine cycle during the time interval tn≤t＜tn+1.(이미지참조) 41

Figure 2.2. Illustration for the engine cycle in the fixed potential-center dynamics. 45

Figure 2.3. Density plot for 〈∆W〉ss in τ → ∞ limit.(이미지참조) 49

Figure 2.4. Density plot for wss in τ → 0 limit.(이미지참조) 52

Figure 2.5. Density plot for 〈∆W〉ss obtained from the truncation method when...(이미지참조) 56

Figure 2.6. Parametric plot for the optimal control parameters (xm*(τ),xf*(τ)). The...(이미지참조) 57

Figure 2.7. Parametric plot for the optimal work per cycle 〈∆W〉ss*. Results ob-...(이미지참조) 59

Figure 2.8. Parametric plot for the optimal power wss∗. Result obtained from the...(이미지참조) 60

Figure 3.1. In the (λw,λQ) plane, we draw schematically the boundary C of the...(이미지참조) 79

Figure 3.2. The LDF for efficiency with the set of parameters K＝1, T₁＝2,... 81

Figure 4.1. Illustration of the link rewiring rule with q＝2. Two quartets sharing... 95

Figure 4.2. Fixed point analysis for q＝4 and βL ≡ 1/TL＝0.1. Nullclines with...(이미지참조) 103

Figure 4.3. Fixed point analysis for q＝4 and βL＝0.3. Nullclines at (a) βs＝0.35,...(이미지참조) 105

Figure 4.4. Phase diagram at q＝4. The solid line is the continuous phase transi-... 109

Figure 4.5. Finite size scaling analysis of (a) the spontaneous magnetization m0...(이미지참조) 111

Figure 4.6. Tricritical scaling of the spontaneous magnetization m0 along the line...(이미지참조) 112

Figure 4.7. Heat flux from the heat bath BL at the infinite temperature for q＝3...(이미지참조) 115