In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the $\alpha$ -total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe.

Resonant tunnelling in a double-barrier heterostructure (DBHS) designed in order to produce an intense coherent emission of phonons is studied theoretically. This emission is achieved when the energy difference between the first excited level and the ground state in the well is close to the LO-phonon energy. The LO phonons emitted during the electron transition decay into a pair of ( and TA) phonons that leave the well in the [111] direction. These secondary TA phonons are coherent and form a beam that we call a SASER (by analogy with `laser'). The circulating current and the populations of phonons and electrons in the well are calculated by solving appropriate kinetic equations. Some possible applications of this system are discussed.