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. The basic variables describing the system are no longer the equilibrium conserved variables: the latter are complemented by non-equilibrium quantities taking the form of flux heat, the viscous pressure tensor, the flux of matter, the flux of electric current, etc. The statements behind extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications such as hyperbolic heat conduction, rheological models, waves in fluids, generalized hydrodynamics, phase diagrams of solutions under shear, non-Fickian diffusion, electrical systems, and a relativistic formulation including some cosmological applications. The book also contains a wide discussion of the foundations and the scope of the most current theories on non-equilibrium thermodynamics (classical irreversible thermodynamics and rational thermodynamics).
The new edition reflects new developments in theory and applications, adds new problems, and contains a new chapter on the interplay between hydrodynamics and thermodynamics, a field of active 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.

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.- 1.4 Rational Thermodynamics.- Problems.- References.- 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.- References.- 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.- 3.7 Beyond the Thirteen-Moment Approximation: Continued-Fraction Expansions of Transport Coefficients.- Problems.- References.- 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.- References.- 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.- 5.6 Relativistic Gas Under an Energy Flow.- Problems.- References.- 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 Flow.- 6.6 Heat Conduction in a Rotating Rigid Cylinder.- 6.7 The Second Law in Non-equilibrium Situations: a Simple Illustration.- 6.8 Non-linear Heat Transfer: Flux Limiters.- 6.9 Other Applications.- Problems.- References.- 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.- References.- 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.- References.- 9 Generalized Hydrodynamics and Computer Simulations.- 9.1 Generalized Hydrodynamics. Density and Current Correlation Functions.- 9.2 Spectral Density Correlation.- 9.3 The Transverse Velocity Correlation Function: the EIT Description.- 9.4 The Longitudinal Velocity Correlation Function: the EIT Description.- 9.5 Computer Simulations of Non-equilibrium Steady States.- Problems.- References.- 10 Non-classical Diffusion and Electrical Conduction.- 10.1 Extended Thermodynamics of Diffusion.- 10.2 Telegrapher's Equation and Stochastic Processes.- 10.3 Taylor Dispersion.- 10.4 Non-Fickian Diffusion in Polymers.- 10.5 Electrical Systems.- 10.6 Cross Terms in Constitutive Equations: Onsager's Relations.- 10.7 Hydrodynamical Models of Transport in Semiconductors.- Problems.- References.- 11 Thermodynamics Under Flow.- 11.1 The Chemical Potential Under Shear. Flow-Induced Changes in the Phase Diagram of Solutions.- 11.2 Explicit Solution for the Rouse-Zimm Model.- 11.3 Chemical Reactions Under Flow: Polymer Degradation.- 11.4 Dynamical Approach.- Problems.- References.- 12 Relativistic Formulation and Cosmological Applications.- 12.1 The Macroscopic Theory.- 12.2 Characteristic Speeds.- 12.3 The Relativistic Kinetic Theory.- 12.4 Cosmological Applications: Viscous Models.- 12.5 Extended Thermodynamics and Cosmological Horizons.- 12.6 Other Applications: Nuclear Collisions.- Problems.- References.- Appendices.- A. Summary of Vector and Tensor Notation.- B. Useful Integrals in the Kinetic Theory of Gases.- C. Some Physical Constants.