Pure-jump processes and constitutive equations for simple thermodinamic bodies with fading memory

Can it be useful to use discontinuous jump-processes in order to formulate a somewhat different thermodynamic theory for a general simple body with fading memory? In this communication I will present the results of paper [9], where the above question is investigated. By means of a certain well defined class of quasi-processes of local pure-jump, there I set up a thermodynamic theory T* for such a body in which only the dynamic part of entropy is assumed to exist.