  In the present paper our aim is to introduce some models for the
generalization of the kinetic theory of electrons and phonons (KTEP), as well
as to study equilibrium solutions and their stability for the generalized KTEP
(GKTEP) equations. We consider a couple of models, relevant to non standard
quantum statistics, which give rise to inverse power law decays of the
distribution function with respect to energy. In the case of electrons in a
phonon background, equilibrium and stability are investigated by means of
Lyapounov theory. Connections with thermodynamics are pointed out.
