Extended Irreversible Thermodynamics

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.