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.

Inhalt

1 Tour d'Horizon.- 2 Early Version of Extended Thermodynamics and Kinetic Theory of Gases.- 1 Paradoxes of Heat Conduction and Shear Diffusion.- 1.1 Heuristic Derivation of the Laws of Fourier and Navier-Stokes.- 1.2 Parabolic Laws of Heat Conduction and Shear Diffusion.- 2 Paradox Removed.- 2.1 The Cattaneo Equation.- 2.2 Extended TIP.- 2.3 Finite Pulse Speeds in Extended TIP.- 2.4 Conclusion and Criticism.- 3 Kinetic Theory of Monatomic Gases.- 3.1 Boltzmann Equation and Moments.- 3.2 Equations of Balance for Moments.- 3.3 Balance of Entropy and Possible Equilibria.- 3.4 The Grad Distribution.- 3.5 Entropy and Entropy Flux in Grad's 13-Moment Theory.- 3.6 Phenomenological Equations derived from the Kinetic Theory.- 3.7 Pulse Speeds.- 3.8 Conclusions.- 3 Formal Structure of Extended Thermodynamics.- 1 Field Equations.- 1.1 Thermodynamic Processes and Principles of the Constitutive Theory.- 1.2 Universal Principles of the Constitutive Theory.- 2 Entropy Inequality and Symmetric Hyperbolic Systems.- 2.1 Exploitation of the Entropy Inequality.- 2.2 Symmetric Hyperbolic Field Equations.- 2.3 Discussion.- 2.4 Characteristic Speeds.- 3 Main Subsystems.- 3.1 Constraints on the Main Field.- 3.2 A Main Subsystem Implies an Entropy Inequality.- 3.3 A Main Subsystem Is Symmetric Hyperbolic.- 3.4 Characteristic Speeds of the Subsystems.- 3.5 Other Subsystems.- 4 Galilean Invariance.- 4.1 Tensors, Galilean Tensors, and Euclidean Tensors.- 4.2 Principle of Relativity.- 4.3 Exploitation of the Principle of Relativity for the Entropy Balance.- 4.4 Exploitation of the Principle of Relativity for the Field Equations.- 4.5 Field Equations for Internal Quantities.- 4.6 Galilei Invariance for Subsystems.- 4.7 Galilean Invariance and Entropy Principle.- 4.8 Explicit Velocity Dependence of Constitutive Quantities. The Determination of Ar.- 5 Thermodynamics of an Euler Fluid.- 5.1 The Euler Fluid.- 5.2 Lagrange Multipliers.- 5.3 Internal Lagrange Multipliers.- 5.4 Absolute Temperature.- 5.5 Vector Potential.- 5.6 Convexity.- 5.7 Characteristic Speed.- 5.8 Subsystems.- 5.9 Discussion.- 4 Extended Thermodynamics of Monatomic Gases.- 1 The Equations of Extended Thermodynamics of Monatomic Gases.- 1.1 Thermodynamic Processes.- 1.2 Discussion.- 1.3 Galilean Invariance. Convective and Nonconvective Fluxes.- 1.4 Euclidean Invariance. Inertial Effects.- 2 Constitutive Theory.- 2.1 Restrictive Principles.- 2.2 Exploitation of the Principle of Material Frame-Indifference.- 2.3 Exploitation of the Entropy Principle.- 2.4 Exploitation of the Requirement of Convexity and Causality.- 3 Field Equations and the Thermodynamic Limit.- 3.1 Field Equations.- 3.2 The Thermodynamic Limit.- 3.3 The Frame Dependence of the Heat Flux.- 3.4 Material Frame Indifference in Ordinary and Extended Thermodynamics.- 4 Thermal Equations of State and Ideal Gases.- 4.1 The Classical Ideal Gas.- 4.2 Comparison with the Kinetic Theory.- 4.3 Comparison with Extended TIP.- 4.4 Degenerate Ideal Gases.- 5 Thermodynamics of Mixtures of Euler Fluids.- 1 Ordinary Thermodynamics of Mixtures (TIP).- 1.1 Constitutive Equations.- 1.2 Paradox of Diffusion.- 2 Extended Thermodynamics of Mixtures of Euler Fluids.- 2.1 Balance Equations.- 2.2 Thermodynamic Processes.- 2.3 Constitutive Theory.- 2.4 Summary of Results.- 2.5 Wave Propagation in a Nonreacting Binary Mixture.- 2.6 Landau Equations. First and Second Sound in He II.- 3 Ordinary and Extended Thermodynamics of Mixtures.- 3.1 The Laws of Fick and Fourier in Extended Thermodynamics.- 3.2 Onsager Relations.- 3.3 Inertial Contribution to the Laws of Diffusion.- 6 Relativistic Thermodynamics.- 1 Balance Equations and Constitutive Restrictions.- 1.1 Thermodynamic Processes.- 1.2 Principles of the Constitutive Theory.- 2 Constitutive Theory.- 2.1 Scope and Structure.- 2.2 Lagrange Multipliers and the Vector Potential. Step i.- 2.3 Principle of Relativity and Linear Representations. Step ii.- 2.4 Stress Deviator, Heat Flux, and Dynamic Pressure. Step iii.- 2.5 Fugacity and Absolute Temperature. Step iv.- 2.6 Linear Relations Between Lagrange Multipliers and n,UA, t(AB),?,qA,e. Step v.- 2.7 The Linear Flux Tensor. Step vi.- 2.8 The Entropy Flux Vector. Step vii.- 2.9 Residual Inequality Step viii.- 2.10 Causality and Convexity. Step ix.- 2.11 Summary of Results. Step x.- 3 Identification of Viscosities and Heat-Conductivity.- 3.1 Extended Thermodynamics and Ordinary Thermodynamics.- 3.2 Transition from Extended to Ordinary Thermodynamics.- 4 Specific Results for Relativistic and Degenerate Gases.- 4.1 Equilibrium Distribution Function.- 4.2 The Degenerate Relativistic Gas.- 4.3 Nondegenerate Relativistic Gas.- 4.4 Degenerate Nonrelativistic Gas.- 4.5 Nondegenerate Nonrelativistic Gas.- 4.6 Strongly Degenerate Relativistic Fermi Gas.- 4.7 A Remark on the Strongly Degenerate Relativistic Bose Gas.- 4.8 Equilibrium Properties of an Ultrarelativistic Gas.- 5 An Application: The Mass Limit of a White Dwarf.- 6 The Relativistic Kinetic Theory for Nondegenerate Gases.- 6.1 Boltzmann-Chernikov Equation.- 6.2 Equations of Transfer.- 6.3 Equations of Balance for Particle Number, Energy-Momentum, Fluxes, and Entropy.- 6.4 Maxwell-Jüttner Distribution, Equilibrium Properties.- 6.5 Possible Thermodynamic Fields in Equilibrium.- 7 The Nonrelativistic Limit of Relativistic Thermodynamics.- 7.1 The Problem.- 7.2 Variables and Constitutive Quantities.- 7.3 The Dynamic Pressure.- 7.4 Order of Magnitude of the Dynamic Pressure.- 7 Extended Thermodynamics of Reacting Mixtures.- 1 Motivation, Results, and Discussion.- 1.1 Motivation.- 1.2 Results.- 1.3 Discussion.- 2 Fields.- 2.1 A Conventional Choice.- 2.2 Absolute Temperature, Fugacities, and Chemical Affinity.- 2.3 Summary of Fields.- 3 Field Equation.- 3.1 Balance Laws.- 3.2 Constitutive Theory.- 3.3 Principle of Relativity.- 4 Entropy Inequality.- 4.1 Lagrange Multipliers.- 4.2 Exploitation.- 5 Nonrelativistic Limit.- 5.1 Discussion.- 5.2 Dynamic Pressure and Bulk Viscosity.- 5.3 Thermal Conductivity and Viscosity.- 8 Waves in Extended Thermodynamics.- 1 Hyperbolicity and Symmetric Hyperbolic Systems.- 1.1 Hyperbolicity in the t-direction.- 1.2 Symmetric Hyperbolic Systems.- 2 Linear Waves.- 2.1 Plane Harmonic Waves, the Dispersion Relation.- 2.2 The High-Frequency Limit.- 2.3 Higher-Order Te…