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## Overview

The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena — non-equilibrium thermodynamics.

S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dynamics, relaxation phenomena, acoustical relaxation, and the behavior of systems in an electromagnetic field.

The statistical foundations of non-equilibrium thermodynamics are treated in detail, and there are special sections on fluctuation theory, the theory of stochastic processes, the kinetic theory of gases, and the derivation of the Onsager reciprocal relations. The implications of causality conditions and of dispersion relations are analyzed in depth.

Advanced students will find a great number of challenging problems, with hints for their solutions. Chemists will be especially interested in the applications to electrochemistry and the theory of chemical reactions. Physicists, teachers, scholars, biologists, and anyone interested in the principle and modern applications of non-equilibrium thermodynamics will find this classic monograph an invaluable reference.

## Product Details

ISBN-13: | 9780486647418 |
---|---|

Publisher: | Courier Corporation |

Publication date: | 02/17/2011 |

Series: | Dover Books on Physics Series |

Pages: | 528 |

Product dimensions: | 5.50(w) x 8.50(h) x 1.06(d) |

## Read an Excerpt

The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena — non-equilibrium thermodynamics.

S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dynamics, relaxation phenomena, acoustical relaxation, and the behavior of systems in an electromagnetic field.

The statistical foundations of non-equilibrium thermodynamics are treated in detail, and there are special sections on fluctuation theory, the theory of stochastic processes, the kinetic theory of gases, and the derivation of the Onsager reciprocal relations. The implications of causality conditions and of dispersion relations are analyzed in depth.

Advanced students will find a great number of challenging problems, with hints for their solutions. Chemists will be especially interested in the applications to electrochemistry and the theory of chemical reactions. Physicists, teachers, scholars, biologists, and anyone interested in the principle and modern applications of non-equilibrium thermodynamics will find this classic monograph an invaluable reference.

## First Chapter

The study of thermodynamics is especially timely today, as its concepts are being applied to problems in biology, biochemistry, electrochemistry, and engineering. This book treats irreversible processes and phenomena — non-equilibrium thermodynamics.

S. R. de Groot and P. Mazur, Professors of Theoretical Physics, present a comprehensive and insightful survey of the foundations of the field, providing the only complete discussion of the fluctuating linear theory of irreversible thermodynamics. The application covers a wide range of topics: the theory of diffusion and heat conduction, fluid dynamics, relaxation phenomena, acoustical relaxation, and the behavior of systems in an electromagnetic field.

The statistical foundations of non-equilibrium thermodynamics are treated in detail, and there are special sections on fluctuation theory, the theory of stochastic processes, the kinetic theory of gases, and the derivation of the Onsager reciprocal relations. The implications of causality conditions and of dispersion relations are analyzed in depth.

Advanced students will find a great number of challenging problems, with hints for their solutions. Chemists will be especially interested in the applications to electrochemistry and the theory of chemical reactions. Physicists, teachers, scholars, biologists, and anyone interested in the principle and modern applications of non-equilibrium thermodynamics will find this classic monograph an invaluable reference.

## Table of Contents

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

## Reading Group Guide

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

## Interviews

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

## Recipe

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