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.- 2 Extended Irreversible Thermodynamics: Evolution Equations.- 2.1 Heat Conduction.- 2.2 One-component Viscous Fluid.- 2.3 The Generalised Entropy Flux and Entropy Production.- 2.4 Linearized Evolution Equations of the Fluxes.- 2.5 Rational Extended Thermodynamics.- 2.6 Some Comments and Perspectives.- 2.7 Entropy Evolution in an Isolated System: An Illustrative Example.- Problems.- 3 Extended Irreversible Thermodynamics: Non-equilibrium Equations of State.- 3.1 Physical Interpretation of the Non-equilibrium Entropy.- 3.2 Non-equilibrium Equations of State: Temperature.- 3.3 Non-equilibrium Equations of State: Thermodynamic Pressure.- 3.4 Convexity Requirements and Stability.- Problems.- 4 Hamiltonian Formulations.- 4.1 GENERIC Formulation.- 4.2 Reversible and Irreversible Kinematics.- 4.3 Governing Equations of EIT.- Problems.- II. Microscopic Foundations.- 5 The Kinetic Theory of Gases.- 5.1 The Basic Concepts of Kinetic Theory.- 5.2 Non-equilibrium Entropy and the Entropy Flux.- 5.3 Grad' Solution.- 5.4 The Relaxation-Time Approximation.- 5.5 Dilute Non-ideal Gases.- 5.6 Non-linear Transport.- 5.7 Beyond the Thirteen-Moment Approximation: Continued-Fraction Expansions of Transport Coefficients.- Problems.- 6 Fluctuation Theory.- 6.1 Einstein' Formula. Second Moments of Equilibrium Fluctuations.- 6.2 Ideal Gases.- 6.3 Fluctuations and Hydrodynamic Stochastic Noise.- 6.4 The Entropy Flux.- 6.5 Application to a Radiative Gas.- 6.6 Onsager' Relations.- Problems.- 7 Information Theory.- 7.1 Basic Concepts.- 7.2 Ideal Gas Under Heat Flux and Viscous Pressure.- 7.3 Ideal Gas Under Shear Flow: Non-linear Analysis.- 7.4 Ideal Gas Submitted to a Heat Flux: Non-linear Analysis.- 7.5 Relativistic Ideal Gas Under an Energy Flow.- 7.6 Heat Flow in a Linear Harmonic Chain.- 7.7 Information Theory and Non-equilibrium Fluctuations.- Problems.- 8 Linear Response Theory.- 8.1 Projection Operator Methods.- 8.2 Evolution Equations for Simple Fluids.- 8.3 Continued-Fraction Expansions.- Problems.- 9 Computer Simulations.- 9.1 Computer Simulations of Non-equilibrium Steady States.- 9.2 Non-equilibrium Equations of State.- 9.3 Dependence of the Free Energy on the Shear Rate: Non-linear Approach.- 9.4 Shear-Induced Heat Flux and the Zeroth Law.- Problems.- III. Selected Applications.- 10 Hyperbolic Heat Conduction.- 10.1 The Finite Speed of Thermal Signals. Second Sound.- 10.2 Heat Pulses.- 10.3 Beyond the Maxwell-Cattaneo Equation.- 10.4 Second Sound Under a Heat Flow.- 10.5 Heat Conduction in a Rotating Rigid Cylinder.- 10.6 Non-linear Heat Transfer: Flux Limiters.- 10.7 Other Applications.- Problems.- 11 Waves in Fluids.- 11.1 Hydrodynamic Modes in Simple Fluids.- 11.2 Transverse Viscoelastic Waves.- 11.3 Ultrasound Propagation in Monatomic Gases.- 11.4 Shock Waves.- Problems.- 12 Generalised Hydrodynamics.- 12.1 Density and Current Correlation Functions.- 12.2 Spectral Density Correlation.- 12.3 The Transverse Velocity Correlation Function: the EIT Description.- 12.4 The Longitudinal Velocity Correlation Function: the EIT Description.- 12.5 Influence of Higher-order Fluxes.- Problems.- 13 Non-classical Diffusion.- 13.1 Extended Thermodynamics of Diffusion.- 13.2 Telegrapher' Equation and Stochastic Processes.- 13.3 Taylor' Dispersion.- 13.4 Non-Fickian Diffusion in Polymers.- 13.5 Hyperbolic Reaction-Diffusion Systems.- Problems.- 14 Electrical Systems.- 14.1 Electrical Systems: Evolution Equations.- 14.2 Cross Terms in Constitutive Equations: Onsager' Relations.- 14.3 Hydrodynamical Models of Transport in Semiconductors and Plasmas.- 14.4 Dielectric Relaxation of Polar Liquids.- Problems.- 15 Rheological Materials.- 15.1 Rheological Models.- 15.2 EIT Description of Linear Visc