Preface

Classical Statistical Dynamics

1.Introduction

2.Probability Theory

2.1 Sample Spaces and States

2.2 Random Variables, Algebras

2.3 Entropy

2.4 Exercises

3.Linear Dynamics

3.1 Reversible Dynamics

3.2 Random Dynamics

3.3 Convergence to Equilibrium

3.4 Markov Chains

3.5 Exercises

4.Isolated Dynamics

4.1 The Boltzmann Map

4.2 The Heat-Particle

4.3 The Hard-Core Model of Chemical Kinetics

4.3.1 Isomers and Diffusion in a Force-Field

4.3.2 Markov Dynamics

4.3.3 Entropy Production

4.3.4 Osmosis

4.3.5 Exchange Diffusion

4.3.6 General Diffusions

4.4 Chemical Reactions

4.4.1 Unimolecular Reactions

4.4.2 Balanced Reactions

4.5 Energy of Solvation

4.6 Activity-led Reactions

4.7 Exercises

5.Isothermal Dynamics

5.1 Legendre Transforms

5.2 The Free-energy Theorem

5.3 Chemical Kinetics

5.4 Convergence in Norm

5.5 Dilation of Markov Chains

5.6 Exercises

6.Driven Systems

6.1 Sources and Sinks

6.2 A Poor Conductor

6.3 A Driven Chemical System

6.4 How to Add Noise

6.5 Exercises

7.Fluid Dynamics

7.1 Hydrostatics of a Gas of Hard Spheres

7.2 The Fundamental Equation

7.3 The Euler Equations

7.4 Entropy Production

7.5 A Correct Navier-Stokes System

Quantum Statistical Dynamics

8.Introduction to Quantum Theory

9.Quantum Probability

9.1 Algebras of Observables

9.2 States

9.3 Quantum Entropy

9.4 Exercises

10.Linear Quantum Dynamics

10.1 Reversible Dynamics

10.2 Random Quantum Dynamics

10.3 Quantum Dynamical Maps

10.4 Exercises

11.Isolated Quantum Dynamics

11.1 The Quantum Boltzmann Map

11.2 The Quantum Heat-Particle

11.3 Fermions and Ions with a Hard Core

11.4 The Quantum Boltzmann Equation

11.5 Exercises

12.Isothermal and Driven Systems

12.1 Isothermal Quantum Dynamics

12.2 Convergence to Equilibrium

12.3 Driven Quantum Systems

12.4 Exercises

13.Infinite Systems

13.1 The Algebra of an Infinite System

13.2 The Reversible Dynamics

13.3 Return to Equilibrium

13.4 Irreversible Linear Dynamics

13.5 Exercises

14.Proof of the Second Law

14.1 yon Neumann Entropy

14.2 Entropy Increase in Quantum Mechanics

14.3 The Quantum Kac Model

14.4 Equilibrium

14.5 The e-Limit

14.6 The Marginals and Entropy

14.7 The Results

15.Information Geometry

15.1 The Jaynes-Ingarden Theory

15.2 Non-Linear Ising Dynamics

15.3 Ising Model Close to Equilibrium

15.4 Non-linear Heisenberg Model

15.5 Estimation; the Cramer-Rao Inequality

15.6 Efron, Dawid and Amari

15.7 Entropy Methods, Exponential Families

15.8 The Work of Pistone and Sempi

15.9 The Finite-Dimensional Quantum Info-Manifold

15.10 Araki's Expansionals and the Analytic Manifold

15.11 The Quantum Young Function

15.12 The Quantum Cramer Class

15.13 The Parameter-Free Quantum Manifold

15.14 Exercises

Bibliography

Index