For the first time the authors' new approach to irreversible thermodynamics, which avoids the assumption of local equilibrium, is presented in detail. The foundations are discussed as well as a host of applications. The book addresses researchers, engineers, and graduate students in thermodynamics

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.

I General Theory.- 1 Classical and Rational Formulations of Non-equilibrium Thermodynamics.- 1.1 The General Balance Laws of Continuum Physics.- 1.2 The Law of Balance of Entropy.- 1.3 Classical Irreversible Thermodynamics (CIT).- 1.4 Rational Thermodynamics.- Problems.- 2 Extended Irreversible Thermodynamics.- 2.1 The Generalized Gibbs Equation.- 2.2 The Generalized Entropy Flux and Entropy Production.- 2.3 Evolution Equations of the Fluxes.- 2.4 Non-equilibrium Equations of State and Convexity Requirements.- 2.5 A Physical Interpretation of the Non-equilibrium Entropy.- 2.6 An Axiomatic Formulation of EIT.- 2.7 Some Comments and Perspectives.- Problems.- II Microscopic Foundations.- 3 The Kinetic Theory of Gases.- 3.1 The Basic Concepts of Kinetic Theory.- 3.2 Non-equilibrium Entropy and the Entropy Flux.- 3.3 Grad's Solution.- 3.4 The Relaxation-Time Approximation.- 3.5 Dilute Non-ideal Gases.- 3.6 Non-linear Transport.- Problems.- 4 Fluctuation Theory.- 4.1 Einstein's Formula. Second Moments of Equilibrium Fluctuations.- 4.2 Ideal Gases.- 4.3 Fluctuations and Hydrodynamic Stochastic Noise.- 4.4 The Entropy Flux.- 4.5 Application: Radiative Gas.- 4.6 Onsager's Relations.- Problems.- 5 Non-equilibrium Statistical Mechanics.- 5.1 Projection Operator Methods.- 5.2 Evolution Equations for Simple Fluids.- 5.3 The Information-Theory Approach.- 5.4 The Ideal Gas Under Heat Flux and Viscous Pressure.- 5.5 Heat Flow in a Linear Harmonic Chain.- Problems.- III Selected Applications.- 6 Hyperbolic Heat Conduction.- 6.1 The Finite Speed of Thermal Signals. Second Sound.- 6.2 Heat Pulses.- 6.3 Phonon Hydrodynamics. Poiseuille Phonon Flow in Solids.- 6.4 Non-equilibrium Absolute Temperature.- 6.5 Second Sound Under a Heat Flux.- 6.6 Heat Conduction in a Rotating Rigid Cylinder.- 6.7 The Second Law in Non-equilibium Situations: a Simple Illustration.- Problems.- 7 Rheological Materials.- 7.1 Rheological Models.- 7.2 Extended Thermodynamic Description of Linear Viscoelasticity.- 7.3 The Rouse-Zimm Relaxational Model.- 7.4 Extended Irreversible Thermodynamics of Second-Order Non-Newtonian Fluids.- Problems.- 8 Waves in Fluids.- 8.1 Hydrodynamic Modes in Simple Fluids.- 8.2 Transverse Viscoelastic Waves.- 8.3 Ultrasound Propagation in Monatomic Gases.- 8.4 Shock Waves.- Problems.- 9 Generalized Hydrodynamics and Computer Simulations.- 9.1 Generalized Hydrodynamics.- 9.2 Density and Current Correlation Functions.- 9.3 Spectral Density Correlation.- 9.4 The Transverse Velocity Correlation Function: the EIT Description.- 9.5 The Longitudinal Velocity Correlation Function: the EIT Description.- 9.6 Computer Simulations of Non-equilibrium Steady States.- Problems.- 10 Multicomponent Systems.- 10.1 Extended Thermodynamics of Diffusion.- 10.2 Continued-Fraction Expansions of Transport Coefficients.- 10.3 The Chemical Potential Under Shear. Flow-induced Changes in the Phase Diagram of Solutions.- 10.4 Electrical Systems.- 10.5 Cross Terms in Constitutive Equations: Onsager's Relations.- Problems.- 11 Relativistic Formulation and Cosmological Applications.- 11.1 The Macroscopic Theory.- 11.2 Characteristic Speeds.- 11.3 The Relativistic Kinetic Theory.- 11.4 Cosmological Applications.- 11.5 Extended Thermodynamics and Cosmological Horizons.- 11.6 Other Applications.- Problems.- References.