统计力学 非平衡态热力学的随机方法 第2版 英文PDF电子书下载

Classical Statistical Dynamics 1

1．Introduction 3

2．Probability Theory 13

2.1 Sample Spaces and States 13

2.2 Random Variables,Algebras 24

2.3 Entropy 34

2.4 Exercises 39

3．Linear Dynamics 43

3.1 Reversible Dynamics 43

3.2 Random Dynamics 48

3.3 Convergence to Equilibrium 60

3.4 Markov Chains 66

3.5 Exercises 69

4． Isolated Dynamics 73

4.1 The Boltzmann Map 73

4.2 The Heat-Particle 87

4.3 The Hard-Core Model of Chemical Kinetics 94

4.3.1 Isomers and Diffusion in a Force-Field 95

4.3.2 Markov Dynamics 100

4.3.3 Entropy Production 102

4.3.4 Osmosis 103

4.3.5 Exchange Diffusion 104

4.3.6 General Diffusions 105

4.4 Chemical Reactions 106

4.4.1 Unimolecular Reactions 106

4.4.2 Balanced Reactions 107

4.5 Energy of Solvation 111

4.6 Activity-led Reactions 111

4.7 Exercises 119

5．Isothermal Dynamics 123

5.1 Legendre Transforms 124

5.2 The Free-energy Theorem 126

5.3 Chemical Kinetics 130

5.4 Convergence in Norm 137

5.5 Dilation of Markov Chains 146

5.6 Exercises 149

6．Driven Systems 151

6.1 Sources and Sinks 151

6.2 A Poor Conductor 152

6.3 A Driven Chemical System 155

6.4 How to Add Noise 162

6.5 Exercises 165

7．Fluid Dynamics 167

7.1 Hydrostatics of a Gas of Hard Spheres 168

7.2 The Fundamental Equation 171

7.3 The Euler Equations 177

7.4 Entropy Production 178

7.5 A Correct Navier-Stokes System 181

Quantum Statistical Dynamics 187

8．Introduction to Quantum Theory 189

9．Quantum Probability 197

9.1 Algebras of Observables 197

9.2 States 204

9.3 Quantum Entropy 213

9.4 Exercises 217

10．Linear Quantum Dynamics 221

10.1 Reversible Dynamics 221

10.2 Random Quantum Dynamics 224

10.3 Quantum Dynamical Maps 228

10.4 Exercises 236

11．Isolated Quantum Dynamics 237

11.1 The Quantum Boltzmann Map 237

11.2 The Quantum Heat-Particle 240

11.3 Fermions and Ions with a Hard Core 256

11.4 The Quantum Boltzmann Equation 272

11.5 Exercises 281

12．Isothermal and Driven Systems 283

12.1 Isothermal Quantum Dynamics 283

12.2 Convergence to Equilibrium 289

12.3 Driven Quantum Systems 292

12.4 Exercises 296

13．Infinite Systems 297

13.1 The Algebra of an Infinite System 299

13.2 The Reversible Dynamics 300

13.3 Return to Equilibrium 302

13.4 Irreversible Linear Dynamics 306

13.5 Exercises 309

14．Proof of the Second Law 311

14.1 von Neumann Entropy 311

14.2 Entropy Increase in Quantum Mechanics 312

14.3 The Quantum Kac Model 314

14.4 Equilibrium 315

14.5 The ？-Limit 316

14.6 The Marginals and Entropy 316

14.7 The Results 317

15．Information Geometry 319

15.1 The Jaynes-Ingarden Theory 319

15.2 Non-Linear Ising Dynamics 322

15.3 Ising Model Close to Equilibrium 327

15.4 Non-linear Heisenberg Model 329

15.5 Estimation;the Cramér-Rao Inequality 333

15.6 Efron,Dawid and Amari 337

15.7 Entropy Methods,Exponential Families 340

15.8 The Work of Pistone and Sempi 341

15.9 The Finite-Dimensional Quantum Info-Manifold 346

15.10 Araki's Expansionals and the Analytic Manifold 352

15.11 The Quantum Young Function 354

15.12 The Quantum Cramér Class 359

15.13 The Parameter-Free Quantum Manifold 360

15.14 Exercises 364

Bibliography 367

Index 377