Generalized kinetic theory of electrons and phonons: models, equilibrium, stability

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.