Non-equilibrium temperature and reference equilibrium values of hidden and internal variables

In previous papers the concepts of caloric and entropic temperatures were outlined and illustrated in a few examples (ideal gas, ideal systems with two or three energy levels, solids with defects or dislocations). In equilibrium states, all degrees of freedom are at the same temperature, but out equilibrium they have different non-equilibrium temperatures. In this work, using a systematic methodology of classical irreversible thermodynamics, we take into consideration an undeformable medium in which the contributions of microscopic phenomena to the macroscopic specific internal energy U can be described by introducing two internal variables and one hidden variable. Internal variables are measurable (from the thermal point of view, they exchange directly heat with the system acting as thermometer) but not controllable, whereas (in our proposal) hidden variables are also not controllable but, in addition, they do not exchange directly heat with the thermometer, but only with other variables. The aim of this paper is to explore the difference between internal and hidden variables and to establish connections and relations among their corresponding non-equilibrium temperatures and the equilibrium temperature of the medium under consideration.