Comment I on "Possible experiment to check the reality of a nonequilibrium temperature"

where s,z(u) is the local-equilibrium entropy, T the local-equilibrium absolute temperature, q the heat flux, A, Some of the most basic questions in nonequilibrium thermodynamics are those concerning the fundamental thermodynamic concepts, namely, the definition and meaning of entropy and of absolute temperature out of equilibrium. Most of the nonequilibrium thermodynamic theories have assumed that these concepts do not need any reformulation out of equilibrium, and that the usual equilibrium concepts may be applied locally in nonhomogeneous nonequilibrium situations. For some years, we have proposed a nonequilibrium absolute temperature [1—4] stemming as the partial derivative of a nonequilibrium entropy that incorporates as variables the dissipative fluxes, in the framework of the so-called extended irreversible thermodynamics (EIT) [5—10]. Up to now, we have analyzed such a nonequilibrium temperature from a theoretical point of view, either from a formal point of view involving dissipative Carnot cycles [2] or, from a more specific point of view, by studying some of the possible indirect consequences of such a generalized temperature in the propagation of heat waves in nonequilibrium steady states [3,4] or in the apparent thermal conductivity in Poiseuille phonon flow [4]. The purpose of this paper is to suggest an experiment to directly check the physical reality of such a nonequilibrium temperature. First of all, we review the introduction of the generalized temperature; afterwards, we suggest the experiment and, finally, we evaluate the order of magnitude of the expected effects. We recall that the standard thermodynamic definition of the absolute temperature is the thermal conductivity, and ~ the relaxation time of the heat flux, defined according to the relaxational evolution equation