This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables are complemented by non-equilibrium quantities. The claims made for extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The present edition reflects new developments in the theory of applications, adds new problems and provides a more detailed comparison with other fields of active research. It contains 130 proposed problems, whose detailed solutions, as well as wide bibliography on extended irreversible thermodynamics and related topices, may be unloaded from the www uab.es/dep-fisica/eit website.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Classical irreversible thermodynamics, as developed by Onsager, Prigogine and many other authors, is based on the local-equilibrium hypothesis. Out of equilibrium, any system is assumed to depend locally on the same set of variables as when it is in eqUilibrium. This leads to a formal thermody­ namic structure identical to that of eqUilibrium: intensive parameters such as temperature, pressure and chemical potentials are well-defined quantities keeping their usual meaning, thermodynamic potentials are derived as Leg­ endre transformations and all equilibrium thermodynamic relations retain their validity. The theory based on this hypothesis has turned out to be very useful and has achieved a number of successes in many practical situations. of interest in going However, the recent decade has witnessed a surge beyond the classical formulation. There are several reasons for this. One of them is the development of experimental methods able to deal with the response of systems to high-frequency and short-wavelength perturbations, such as ultrasound propagation and light and neutron scattering. The ob­ served results have led to generalizations of the classical hydrodynamical theories, by including memory functions or generalized transport coefficients depending on the frequency and the wavevector. This field has generated impressive progress in non-equilibrium statistical mechanics, but for the moment it has not brought about a parallel development in non-equilibrium thermodynamics. An extension of thermodynamics compatible with gener­ alized hydrodynamics therefore appears to be a natural subject of research.

Modern technology strives towards higher speed, higher power, and higher miniaturiza­ tion. In these conditions, the classical transport equations must be updated in order to incorporate memory, non-local, and non-linear effects. These effects have been studied by starting from microscopic models which are specific to particular systems and whose solution requires mathematical approximations and boundary conditions. The aim of extended irreversible thermodynamics is to complement such microscopic analyses with a macroscopic framework which could play, with respect to the generalized trans­ port equations incorporating the aforementioned effects, a role similar to the one played by classical thermodynamics with respect to the classical transport equations. Such a macroscopic framework is particularly useful for comparing the results obtained from various microscopic models, for placing some restrictions on the range of validity of different approximations, and for settling a discussion on some basic concepts that arise unavoidably in a formalism that crosses the frontiers of the local-equilibrium theory. Extended irreversible thermodynamics is not at all in conflict with the classical theory of non-equilibrium thermodynamics and rational thermodynamics but must be viewed as a relevant extension of the scope of these descriptions. For the student or the researcher, it may be stimulating to go beyond the classical theories and to enter a of new ideas, new applications, and new problems.

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables are complemented by non-equilibrium quantities. The claims made for extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The present edition reflects new developments in the theory of applications, adds new problems and provides a more detailed comparison with other fields of active research. It contains 130 proposed problems, whose detailed solutions, as well as wide bibliography on extended irreversible thermodynamics and related topices, may be unloaded from the www uab.es/dep-fisica/eit website.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems. Alloverthiswork,wehavebeenguidedbytheformula: “Getthemorefromtheless”,withthepurposetomakeamaximumofpeople aware of a maximum of knowledge from a minimum of basic tools. Besidesbeinganintroductorytext,ourobjectiveistopresentanoverview, as general as possible, of the more recent developments in non-equilibrium thermodynamics, especially beyond the local equilibrium description.

Classical irreversible thermodynamics, as developed by Onsager, Prigogine and many other authors, is based on the local-equilibrium hypothesis. Out of equilibrium, any system is assumed to depend locally on the same set of variables as when it is in eqUilibrium. This leads to a formal thermody­ namic structure identical to that of eqUilibrium: intensive parameters such as temperature, pressure and chemical potentials are well-defined quantities keeping their usual meaning, thermodynamic potentials are derived as Leg­ endre transformations and all equilibrium thermodynamic relations retain their validity. The theory based on this hypothesis has turned out to be very useful and has achieved a number of successes in many practical situations. of interest in going However, the recent decade has witnessed a surge beyond the classical formulation. There are several reasons for this. One of them is the development of experimental methods able to deal with the response of systems to high-frequency and short-wavelength perturbations, such as ultrasound propagation and light and neutron scattering. The ob­ served results have led to generalizations of the classical hydrodynamical theories, by including memory functions or generalized transport coefficients depending on the frequency and the wavevector. This field has generated impressive progress in non-equilibrium statistical mechanics, but for the moment it has not brought about a parallel development in non-equilibrium thermodynamics. An extension of thermodynamics compatible with gener­ alized hydrodynamics therefore appears to be a natural subject of research.

Modern technology strives towards higher speed, higher power, and higher miniaturiza­ tion. In these conditions, the classical transport equations must be updated in order to incorporate memory, non-local, and non-linear effects. These effects have been studied by starting from microscopic models which are specific to particular systems and whose solution requires mathematical approximations and boundary conditions. The aim of extended irreversible thermodynamics is to complement such microscopic analyses with a macroscopic framework which could play, with respect to the generalized trans­ port equations incorporating the aforementioned effects, a role similar to the one played by classical thermodynamics with respect to the classical transport equations. Such a macroscopic framework is particularly useful for comparing the results obtained from various microscopic models, for placing some restrictions on the range of validity of different approximations, and for settling a discussion on some basic concepts that arise unavoidably in a formalism that crosses the frontiers of the local-equilibrium theory. Extended irreversible thermodynamics is not at all in conflict with the classical theory of non-equilibrium thermodynamics and rational thermodynamics but must be viewed as a relevant extension of the scope of these descriptions. For the student or the researcher, it may be stimulating to go beyond the classical theories and to enter a of new ideas, new applications, and new problems.

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.

The fast progress in many areas of research related to non-equilibrium ther- dynamics has prompted us to write a fourth edition of this book. Like in the previous editions, our main concern is to open the subject to the widest au- ence, including students, teachers, and researchers in physics, chemistry, engine- ing, biology, and materials sciences. Our objective is to present a general view on several open problems arising in non-equilibrium situations, and to afford a wide perspective of applications illustrating their practical outcomes and con- quences. A better comprehension of the foundations is generally correlated to an increase of the range of applications, implying mutual feedback and cross fert- ization. Truly, thermodynamic methods are widely used in many areas of science but, surprisingly, the active dynamism of thermodynamics as a ?eld on its own is not suf?ciently perceived outside a relatively reduced number of specialized researchers. Extended irreversible thermodynamics (EIT) goes beyond the classical f- malisms based on the local equilibrium hypothesis; it was also referred to in an earlier publication by the authors (Lebon et al. 1992) as a thermodynamics of the third type, as it provides a bridge between classical irreversible thermodynamics and rational thermodynamics, enlarging at the same time their respective range of application. The salient feature of the theory is that the ?uxes are incorporated into the set of basic variables.