Unified Formulation and Asymptotic Limits of Inhomogeneous Kinetic Models within GENERIC

TL;DR

This paper unifies various inhomogeneous kinetic models within the GENERIC framework, deriving asymptotic limits like Landau equations and demonstrating their GENERIC formulation across classical, relativistic, and quantum contexts.

Contribution

It introduces a unified kinetic model framework in GENERIC and derives asymptotic limits, extending the applicability of GENERIC to new kinetic equations.

Findings

Unified kinetic models in GENERIC framework across multiple physical regimes.

Derived Landau-type equations as grazing limits of the unified models.

Showed limiting systems can also be formulated within GENERIC.

Abstract

In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kinetic Boltzmann equations and the kinetic wave equations, in both classical (non-relativistic), relativistic and quantum settings. We formulate this unified equation into the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework. We then derive the grazing (small-angle) limit in two-body interaction systems, which leads to Landau-type equations. Finally, we show that these limiting systems can also be formulated as GENERIC systems.