Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

Ordinary thermodynamics provides reliable results when the thermodynamic fields are smooth, in the sense that there are no steep gradients and no rapid changes. In fluids and gases this is the domain of the equations of Navier-Stokes and Fourier. Extended thermodynamics becomes relevant for rapidly varying and strongly inhomogeneous processes. Thus the propagation of high frequency waves, and the shape of shock waves, and the regression of small-scale fluctuation are governed by extended thermodynamics. The field equations of ordinary thermodynamics are parabolic while extended thermodynamics is governed by hyperbolic systems. The main ingredients of extended thermodynamics are • field equations of balance type, • constitutive quantities depending on the present local state and • entropy as a concave function of the state variables. This set of assumptions leads to first order quasi-linear symmetric hyperbolic systems of field equations; it guarantees the well-posedness of initial value problems and finite speeds of propaga tion. Several tenets of irreversible thermodynamics had to be changed in subtle ways to make extended thermodynamics work. Thus, the entropy is allowed to depend on nonequilibrium vari ables, the entropy flux is a general constitutive quantity, and the equations for stress and heat flux contain inertial terms. New insight is therefore provided into the principle of material frame indifference. With these modifications an elegant formal structure can be set up in which, just as in classical thermostatics, all restrictive conditions--derived from the entropy principle-take the form of integrability conditions.

This book offers an easy to read, all-embracing history of thermodynamics. It describes the long development of thermodynamics, from the misunderstood and misinterpreted to the conceptually simple and extremely useful theory that we know today. Coverage identifies not only the famous physicists who developed the field, but also engineers and scientists from other disciplines who helped in the development and spread of thermodynamics as well.

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.

This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.

Extended Non-Equilibrium Thermodynamics provides powerful tools departing not from empirical or statistical considerations but from fundamental thermodynamic laws, proposing final solutions that are readily usable and recognizable for students, researchers and industry. The book deals with methods that allow combining easily the present theory with other fields of science, such as fluid and solid mechanics, heat and mass transfer processes, electricity and thermoelectricity, and so on. Not only are such combinations facilitated, but they are incorporated into the developments in such a way that they become part of the theory. This book aims at providing for a systematic presentation of Extended Non-Equilibrium Thermodynamics in nanosystems with a high degree of applicability. Furthermore, the book deals with how physical properties of systems behave as a function of their size. Moreover, it provides for a systematic approach to understand the behavior of thermal, electrical, thermoelectric, photovoltaic and nanofluid properties in nanosystems. Experimental results are used to validate the theory, the comparison is analysed, justified and discussed, and the theory is then again used to understand better experimental observations. The new developments in this book, being recognizable in relation with familiar concepts, should make it appealing for academics and researchers to teach and apply and graduate students to use. The text in this book is intended to bring attention to how the theory can be applied to real-life applications in nanoscaled environments. Case studies, and applications of theories, are explored including thereby nanoporous systems, solar panels, nanomedicine drug permeation and properties of nanoporous scaffolds. Explores new generalized thermodynamic models Provides introductory context of Extended Non-Equilibrium Thermodynamics within classical thermodynamics, theoretical fundamentals and several applications in nanosystems Provides for a systematic approach to understand the behavior of thermal, electric, thermoelectric and viscous properties as a function of several parameters in nanosystems Includes reflections to encourage the reader to think further and put the information into context Examines future developments of new constitutive equations and theories and places them in the framework of real-life applications in the energetic and medical sectors, such as photovoltaic and thermoelectric devices, nanoporous media, drug delivery and scaffolds

Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.

Despite a long history of almost 180 years stretching back to the times of Carnot and, later, Clausius and Lord Kelvin, amongst others following him, the subject of thermodynamics has not as yet seen its full maturity, in the sense that the theory of irreversible processes has remained incomplete. The works of L. Onsager, J. Meixner, I. Prigogine on the thermodyn- ics of linear irreversible processes are, in effect, the early efforts toward the desired goal of giving an adequate description of irreversible processes, but their theory is confined to near-equilibrium phenomena. The works in recent years by various research workers on the extension of the aforem- tioned thermodynamic theory of linear irreversible processes are further efforts toward the goal mentioned. The present work is another of such efforts and a contribution to the subject of generalizing the thermodyn- ics of reversible processes, namely, equilibrium thermodynamics, to that of irreversible processes—non-equilibrium thermodynamics, without being restricted to linear irreversible processes. In this context the terms ‘far - moved from equilibrium’ is often used in the literature, and such states of macroscopic systems and non-linear irreversible phenomena in them are the objects of interest in this work. The thermodynamics of processes, either reversible or irreversible, is a continuum mechanical theory of matter and energy and their exchange between different parts of the system, and as such it makes no direct r- erence to the molecules constituting the substance under consideration.