Generalized Kinetic Theory of Electrons and Phonons: Models, Equilibrium, Stability

TL;DR

This paper introduces generalized models for the kinetic theory of electrons and phonons, explores their equilibrium states, and analyzes their stability using Lyapunov theory, with implications for non-standard quantum statistics and thermodynamics.

Contribution

It presents new generalized kinetic models for electrons and phonons, analyzing equilibrium solutions and stability, extending classical theories to non-standard quantum statistical frameworks.

Findings

Equilibrium solutions are characterized for the generalized models.

Stability of these equilibria is established via Lyapunov methods.

Connections to thermodynamics are discussed.

Abstract

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.