Global equivalence for rigid heat-conducting bodies

In a previous paper of the author, the notion of global equivalence between two deformable thermoelastic bodies B and B' was introduced. This equivale nce is understood in the sense that a global thermokinetic process for B is admissible (in the sense of Coleman and Noll) if and only if its counterpa rt for B, according to a suitable bijective correspondence (k) over cap bet ween B and B', also is admissible. In this case, B and B' are said to be gl obally (k) over cap -equivalent. Global (k) over cap -equivalence does not imply piecewise (k) over cap -equivalence, that is, the global equivalence of arbitrary (k) over cap -corresponding subbodies of B and B'. Here we pre sent two maximality theorems of global equivalence for a rigid heat-conduct ing body B: one in the thermodynamic theory with no heat sources and the ot her in the thermodynamic theory with heat supply. By these theorems, given the rigid heat-conducting body B referred to its configuration (y) over cap , in both the theories we characterize the constitutive equations for all r igid heat conductors B' that have a configuration (y) over cap' with (y) ov er cap'(B') = (y) over cap (B) and are globally (k) over cap -equivalent to B for (k) over cap = (y) over cap (l-1) o (y) over cap.