## Extended thermodynamics.(English)Zbl 0801.35141

Springer Tracts in Natural Philosophy. 37. New York: Springer-Verlag. xi, 230 p. (1993).
It is a fundamental monography successive and systematic expanding of the thermodynamics of irreversible processes. The distinctive feature of the proposal theory is in the replacement of parabolic equations of irreversible thermodynamics – those of Navier-Stokes and Fourier – on the hyperbolic field equations. Such approach removes a familiar paradoxon of heat conduction and shear diffusion consisting in infinitely fast propagation.
The main ingredients of extended thermodynamics are
– field equation 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 mono-atomic gases these variables are thirteen fields of densities, i.e. mass density $$\rho$$, momentum density $$\rho^{v_ i}$$, momentum flux density $$F_{ij}$$, and energy flux density $$1/2 F_{ppi}$$. The necessary field equations are based on the equations of balance of mass, momentum, momentum flux and energy flux. These quasilinear symmetric hyperbolic equations guarantee the well-posedness of initial value problems, and permit 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 brief chapters at the end of the book describe the present status of the systematic theory in the extended thermodynamics of photons and phonons.

### MSC:

 35Q80 Applications of PDE in areas other than physics (MSC2000) 80-02 Research exposition (monographs, survey articles) pertaining to classical thermodynamics 80A10 Classical and relativistic thermodynamics 35L65 Hyperbolic conservation laws 82C40 Kinetic theory of gases in time-dependent statistical mechanics