  Heat conduction is investigated on three levels: equilibrium, Fourier, and
Cattaneo. The Fourier level is either the point of departure for investigating
the approach to equilibrium or the final stage in the investigation of the
approach from the Cattaneo level. Both investigations bring to the Fourier
level an entropy and a thermodynamics. In the absence of external and internal
influences preventing the approach to equilibrium the entropy that arises in
the latter investigation is the production of the classical entropy that arises
in the former investigation. If the approach to equilibrium is prevented, then
the entropy that arises in the investigation of the approach from the Cattaneo
level to the Fourier level still brings to the Fourier level the entropy and
the thermodynamics even if the classical entropy and the classical
thermodynamics is absent. We also note that vanishing total entropy production
as a characterization of equilibrium state is insufficient.
