Rational extended thermodynamics.
2nd ed.

*(English)*Zbl 0895.00005
Springer Tracts in Natural Philosophy. 37. New York, NY: Springer. xv, 396 p. (1998).

For a review of the first ed. (Springer 1993) see Zbl 0801.35141.

This is a fundamental monograph successively and systematically expanding the thermodynamics of irreversible processes. The distinctive feature of the proposed theory lies in the replacement of parabolic equations of irreversible thermodynamics – those of Navier-Stokes and Fourier – by hyperbolic field equations. Such an approach removes the familiar paradox of heat conduction and shear diffusion consisting in infinitely fast propagation.

The main ingredients of extended thermodynamics are

– field equations of balance type;

– constitutive quantities depending on the present local state;

– entropy as a concave function of the state variables.

On the foundation of the theory lies the extended list of variables on which the specific entropy and the entropy flux depend. For example for monatomic gases these variables are thirteen fields of densities, i.e. mass density \(F=\rho\), momentum density \(F_i=\rho v_i\), momentum flux density \(F_{ij}\), and energy flux density \(\frac 12 F_{ppi}\). The necessary field equations are based on the equations of balance of mass, momentum, momentum flux and energy flux. These quasi-linear symmetric hyperbolic equations guarantees the well-posedness of initial value problems and finite speeds of propagation. It also permits the treatment of shock waves.

Extended thermodynamics is most restrictive for gases, or more generally, for bodies whose constituent particles have large mean free paths. Most of this book deals with gases: classical ideal gases, degenerate gases and mixtures of gases. It puts into perspective the various phenomena called second sound, viz. heat propagation, propagation of shear stress, and the second sound in superfluid helium. Two chapters describe the present status of the systematic theory in the extended thermodynamics of photons and phonons.

The present book is a new edition; at least half of the material is new and the rest has been revised and streamlined to a considerable degree.

This is a fundamental monograph successively and systematically expanding the thermodynamics of irreversible processes. The distinctive feature of the proposed theory lies in the replacement of parabolic equations of irreversible thermodynamics – those of Navier-Stokes and Fourier – by hyperbolic field equations. Such an approach removes the familiar paradox of heat conduction and shear diffusion consisting in infinitely fast propagation.

The main ingredients of extended thermodynamics are

– field equations of balance type;

– constitutive quantities depending on the present local state;

– entropy as a concave function of the state variables.

On the foundation of the theory lies the extended list of variables on which the specific entropy and the entropy flux depend. For example for monatomic gases these variables are thirteen fields of densities, i.e. mass density \(F=\rho\), momentum density \(F_i=\rho v_i\), momentum flux density \(F_{ij}\), and energy flux density \(\frac 12 F_{ppi}\). The necessary field equations are based on the equations of balance of mass, momentum, momentum flux and energy flux. These quasi-linear symmetric hyperbolic equations guarantees the well-posedness of initial value problems and finite speeds of propagation. It also permits the treatment of shock waves.

Extended thermodynamics is most restrictive for gases, or more generally, for bodies whose constituent particles have large mean free paths. Most of this book deals with gases: classical ideal gases, degenerate gases and mixtures of gases. It puts into perspective the various phenomena called second sound, viz. heat propagation, propagation of shear stress, and the second sound in superfluid helium. Two chapters describe the present status of the systematic theory in the extended thermodynamics of photons and phonons.

The present book is a new edition; at least half of the material is new and the rest has been revised and streamlined to a considerable degree.

Reviewer: N.E.Ratanov (Chelyabinsk)

##### MSC:

00A79 | Physics |

82-02 | Research exposition (monographs, survey articles) pertaining to statistical mechanics |

80-02 | Research exposition (monographs, survey articles) pertaining to classical thermodynamics |

82C35 | Irreversible thermodynamics, including Onsager-Machlup theory |

76A02 | Foundations of fluid mechanics |

74A15 | Thermodynamics in solid mechanics |

80A10 | Classical and relativistic thermodynamics |

35Q80 | Applications of PDE in areas other than physics (MSC2000) |

35L65 | Hyperbolic conservation laws |

82C40 | Kinetic theory of gases in time-dependent statistical mechanics |