Non-Equilibrium Thermodynamics

PREFACE TABLE OF CONTENTS CHAPTER I INTRODUCTION 1. Historical background of non-equilibrium thermodynamics 2. Systematic development of the theory PART A. GENERAL THEORY CHAPTER II CONSERVATION LAWS 1. Introduction 2. Conservation of mass 3. The equation of motion 4. Conservation of energy CHAPTER III ENTROPY LAW AND ENTROPY BALANCE 1. The second law of thermodynamics 2. The entropy balance equation 3. Alternative expressions for the entropy production; on different definitions of the heat flow 4. Kinetic energy of diffusion CHAPTER IV THE PHENOMENOLOGICAL EQUATIONS 1. The linear laws 2. Influence of symmetry properties of matter on the linear laws; Curie principle 3. The Onsager reciprocal relations 4. The differential equations CHAPTER V THE STATIONARY STATES 1. Introduction 2. Mechanical equilbrium 3. Stationary states with minimum entropy production 4. Stationary states without minimum entropy production CHAPTER VI PROPERTIES OF THE PHENOMENOLOGICAL EQUATIONS AND THE ONSAGER RELATIONS 1. Introduction 2. The Curie principle 3. Dependent fluxes and thermodynamic forces 4. Onsager relations for vectorial (and tensorial) phenomena 5. Transformation properties of the Onsager relations CHAPTER VII DISCUSSION OF THE STATISTICAL FOUNDATIONS 1. Introduction 2. State variables and fluctuations 3. Microscopic reversibility 4. Derivation of the Onsager reciprocal relations 5. Furthr properties of the matrix of phenomenological coefficients 6. Gaussian Markoff processes 7. Gaussian Markoff processes: Langevin equations 8. Entropy and random fluctuations CHAPTER VIII THE FLUCTUATION DISSIPATION THEOREM 1. Introduction 2. The correlation function of stationary processes; the Wiener-Khinchin theorem 3. The principle of casuality; the Kramers-Kronig relations 4. Derivation of the fluctuation dissipation theorem 5. The entropy production in a system subjected to external driving forces CHAPTER IX DISCUSSION OF FOUNDATIONS BY MEANS OF KINETIC THEORY 1. Introduction 2. The Boltzmann equation 3. The hydrodynamic equation 4. The entropy balance equation; Boltmann's H-theorem 5. The Enskog method of solution of the Boltzmann equation 6. The entropy balance equation in the first approximation of Enskog 7. The Onsager relations 8. Brownian motion PART B. APPLICATIONS CHAPTER X CHEMICAL REACTIONS AND RELAXATION PHENOMENA 1. Introduction 2. Chemical reactions 3. Coupled chemical reactions 4. Unimolecular reactions; the principle of detailed balance 5. Relaxation phenomena 6. Internal degrees of freedom "CHAPTER XI HEAT CONDUCTION, DIFFUSION AND CROSS-EFFECTS" 1. Heat conduction 2. Diffusion. General remarks 3. Thermodynamic symmetry relations for chemical potentials 4. Diffusion in binary systems 5. Diffusion in multi-component systems 6. Diffusion in rotating systems 7. Thermal diffusion (Soret effect) and Dufour effect 8. Heat conduction and thermal diffusion in reacting systems CHAPTER XII VISCOUS FLOW AND RELAXATION PHENOMENA 1. Viscous flow in an isotropic fluid 2. Viscous flow in a magnetic field 3. Propagation of sound 4. Acoustical relaxation 5. The influence of viscosity and heat conduction on the propagation of sound 6. Elastic relaxation CHAPTER XIII ELECTRICAL CONDUCTION 1. Introduction 2. The Maxwell equations 3. Conservation laws and entropy balance in systems without polarization 4. Entropy balance (continued) 5. Electric resistance 6. Thermo-electric potential and Peltier effect 7. Galvanomagnetic and thermomagnetic effects 8. Sedimentation potential and electrophoresis 9. Diffusion and thermal diffusion potentials; thermopotential of a thermocell CHAPTER XIV IRREVERSIBLE PROCESSES IN POLARIZED SYSTEMS 1. Conservation laws in polarized systems 2. The entropy balance equation in polarized systems 3. Pressure and ponderomotive force 4. The chemical potential in a polarized medium 5. Dielectric and magnetic relaxation CHAPTER XV DISCONTINUOUS SYSTEMS 1. Introduction 2. Conservation laws 3. Entropy law and entropy balance 4. Phenomenological equations and Onsager reciprocal relations 5. "Thermomolecular pressure effect, thermal effusion and mechano-caloric effect in reacting mixtures" 6. Osmotic pressure and permeability of membranes 7. Electrokinetic effects 8. "Thermomolecular pressure effect, thermal effusion and mechano-caloric effect in reacting mixtures" 9. Electrochemistry APPENDIX I. On Matrix and tensor notation APPENDIX II. On thermodynamic relations APPENDIX III. The Gaussian distribution for macroscopic variables PROBLEMS NAME INDEX SUBJECT INDEX