Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.
Inhaltsverzeichnis
1 Early Version of Extended Thermodynamics and Kinetic Theory of Gases. - 1 Paradoxa of Heat Conduction and Shear Diffusion. - 2 Paradox Removed. - 3 Kinetic Theory of Mon-Atomic Gases. - 2 Extended Thermodynamics of Mon-Atomic Gases. - 1 The Equations of Extended Thermodynamics of Mon-Atomic Gases. - 2 Constitutive Theory. - 3 Field Equations and the Thermodynamic Limit. - 4 Thermal Equations of State and Specific Equation for Ideal Gases. - 3 Thermodynamics of Mixtures of Fluids. - 1 Ordinary Thermodynamics of Mixtures (TIP). - 2 Extended Thermodynamics of Non-Viscous Simple Mixtures. - 3 Ordinary and Extended Thermodynamics of Mixtures. - 4 Relativistic Extended Thermodynamics of Mon-Atomic Gases. - 1 Balance Equations and Constitutive Restrictions. - 2 Constitutive Theory. - 3 Identification of Viscosities and Heat Conductivity. - 4 Specific Results for Relativistic and Degenerate Gases. - 5 Two Applications. - 6 The Relativistic Kinetic Theory for Non-Degenerate Gases. - 7 The Non-Relativistic Limit of Relativistic Thermodynamics. - 5 Thermodynamics of Light and Sound. - 1 Phonons and Photons. - 2 Energy and Momentum of Light and Sound. - 3 Shock Waves. - 6 Formal Structure of Extended Thermodynamics. - 1 The Formal Structure of Extended Thermodynamics. - 2 Galilean Invariance. - 3 Variables of Increasing Tensorial Rank. - 7 Waves in Extended Thermodynamics. - 1 Hyperbolicity and Symmetric Hyperbolic Systems. - 2 Linear Waves. - 3 Hyperbolicity in Extended Thermodynamics. - 4 Non-Linear Waves, Discontinuity Waves, or Acceleration Waves. - 5 Non-Linear Waves and Shock Waves. - 8 Second Sound in Solids at Low Temperature. - 1 Extended Thermodynamics of Phonons Generalized. - 2 Shock Waves in a Rigid Conductor. - 9 Molecular Extended Thermodynamics. - 1 Field Equations of Molecular Extended Thermodynamicsof Many Moments. - 2 More Kinetic Theory. - 3 Equations for Mean Eigenfunctions and Closure. - 4 Molecular Extended Thermodynamics and Method of Eigenfunctions. - 10 Testing Extended Thermodynamics by Light. - 1 Basic Electrodynamics. - 2 Auto-Correlation Function as the Characteristic Feature of a Fluctuating Quantity. - 3 The Spectral Density: A Measurable Quantity. - 4 Onsager Hypothesis. - 5 Auto-Correlation Function and Its Properties. - 6 How to Use Light Scattering. - 7 Light Scattering and Extended Thermodynamics. - 11 Testing Extended Thermodynamics by Sound. - 1 Basic Acoustics. - 2 Dispersion Relations. - 3 Maximum Speed. - 3. 1 Modes of Least Damping. - 3. 2 The Maximum Speed.
