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.