1．Entropy 1
1.1 Statistical Ensembles 1
1.2 Microcanonical Ensemble and Entropy 3
1.3 Thermodynamics 5
1.4 Principle of Maximum Entropy 5
1.5 Example:Defects in Solid 7
2．Maxwell-Boltzmann Distribution 11
2.1 Classical Gas of Atoms 11
2.2 The Most Probable Distribution 12
2.3 The Distribution Function 13
2.4 Thermodynamic Properties 16
3．Free Energy 17
3.1 Canonical Ensemble 17
3.2 Energy Fluctuations 20
3.3 The Free Energy 20
3.4 Maxwell's Relations 23
3.5 Example:Unwinding of DNA 24
4．Chemical Potential 27
4.1 Changing the Particle Number 27
4.2 Grand Canonical Ensemble 28
4.3 Thermodynamics 30
4.4 Critical Fluctuations 30
4.5 Example:Ideal Gas 31
5．Phase Transitions 33
5.1 First-Order Phase Transitions 33
5.2 Second-Order Phase Transitions 34
5.3 Van der Waals Equation of State 37
5.4 Maxwell Construction 40
6．Kinetics of Phase Transitions 43
6.1 Nucleation and Spinodal Decomposition 43
6.2 The Freezing of Water 45
7．The Order Parameter 49
7.1 Ginsburg-Landau Theory 49
7.2 Second-Order Phase Transition 50
7.3 First-Order Phase Transition 51
7.4 Cahn-Hilliard Equation 53
8．Correlation Function 55
8.1 Correlation Length 55
8.2 Large-Distance Correlations 55
8.3 Universality Classes 57
8.4 Compactness Index 58
8.5 Scaling Properties 58
9．Stochastic Processes 61
9.1 Brownian Motion 61
9.2 Random Walk 63
9.3 Diffusion 64
9.4 Central Limit Theorem 65
9.5 Diffusion Equation 65
10．Langevin Equation 67
10.1 The Equation 67
10.2 Solution 68
10.3 Fluctuation-Dissipation Theorem 69
10.4 Power Spectrum and Correlation 69
10.5 Causality 70
10.6 Energy Balance 72
11．The Life Process 75
11.1 Life 75
11.2 Cell Structure 76
11.3 Molecular Interactions 78
11.4 Primary Protein Structure 79
11.5 Secondary Protein Structure 81
11.6 Tertiary Protein Structure 82
11.7 Denatured State of Protein 84
12．Self-Assembly 85
12.1 Hydrophobic Effect 85
12.2 Micelles and Bilayers 87
12.3 Cell Membrane 88
12.4 Kinetics of Self-Assembly 90
12.5 Kinetic Arrest 92
13．Kinetics of Protein Folding 95
13.1 The Statistical View 95
13.2 Denatured State 96
13.3 Molten Globule 97
13.4 Folding Funnel 101
13.5 Convergent Evolution 101
14．Power Laws in Protein Folding 105
14.1 The Universal Range 105
14.2 Collapse and Annealing 106
14.3 Self-Avoiding Walk(SAW) 108
15．Self-Avoiding Walk and Turbulence 113
15.1 Kolmogorov's Law 113
15.2 Vortex Model 113
15.3 Quantum Turbulence 116
15.4 Convergent Evolution in Turbulence 117
16．Convergent Evolution in Protein Folding 119
16.1 Mechanism of Convergent Evolution 119
16.2 Energy Cascade in Turbulence 120
16.3 Energy Cascade in the Polymer Chain 120
16.4 Energy Cascade in the Molten Globule 122
16.5 Secondary and Tertiary Structures 123
A．Model of Energy Cascade in a Protein Molecule 125
A.1 Brownian Motion of a Forced Harmonic Oscillator 125
A.2 Coupled Oscillators 127
A.2.1 Equations of Motion 127
A.2.2 Energy Balance 129
A.2.3 Fluctuation-Dissipation Theorem 130
A.2.4 Perturbation Theory 130
A.2.5 Weak-Damping Approximation 131
A.3 Model of Protein Dynamics 132
A.4 Fluctuation-Dissipation Theorem 135
A.5 The Cascade Time 136
A.6 Numerical Example 137
Index 141